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123 results on '"Cossart, Vincent"'

1. Constancy of the Hilbert-Samuel function

Author

Cossart, Vincent, Piltant, Olivier, and Schober, Bernd

Subjects
Mathematics - Algebraic Geometry
Abstract

The Hilbert-Samuel function and the multiplicity function are fundamental locally defined invariants on Noetherian schemes. They have been playing an important role in desingularization for many years. Bennett studied upper semicontinuity of the Hilbert-Samuel function on schemes and proved that it is non increasing under permissible blowing ups. The latter are blowing ups at regular subschemes along which the singular scheme is normally flat. For a reduced scheme, the Hilbert-Samuel function is constant if and only if it is regular: this translates the question of resolution of singularities into a problem of lowering the Hilbert-Samuel function. We show here that this result can be extended to non reduced schemes as follows: Given a locally Noetherian scheme X such that the local rings are excellent for every point, then the Hilbert-Samuel function is constant on X if and only if X is normally flat along its reduction and the reduction itself is regular.

Published
2023

3. Invariance of Hironaka's characteristic polyhedron

Author

Cossart, Vincent, Jannsen, Uwe, and Schober, Bernd

Subjects
Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra
Abstract

We show that given a face of Hironaka's characteristic polyhedron, it does only depend on the singularity and a flag defined by the linear form determining the face. As a consequence we get that certain numerical data obtained from the characteristic polyhedron are invariants of the singularity. In particular, they do not depend on an embedding., Comment: 29 pages, 5 figures

Published
2018

4. -Permissible Blow-Ups: The Non-embedded Case

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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5. (u)-standard Bases

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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6. Main Theorems and Strategy for Their Proofs

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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7. Transformation of Standard Bases Under Blow-Ups

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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8. Characteristic Polyhedra of J ⊂ R

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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9. An Alternative Proof of Theorem 6.17

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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10. Appendix. Hironaka’s Characteristic Polyhedron. Notes for Novices(B.Schober)

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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11. Permissible Blow-Ups

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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12. Basic Invariants for Singularities

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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13. -Permissible Blow-Ups: The Embedded Case

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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14. Introduction

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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15. Functoriality, Locally Noetherian Schemes, Algebraic Spaces and Stacks

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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16. Proof in the Case e x (X) = es x (X) = 2 , I: Some Key Lemmas

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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17. Non-existence of Maximal Contact in Dimension 2

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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18. Proof in the Case e x (X) = e x (X) = 2 , III: Inseparable Residue Extensions

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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19. Proof in the Case , II: Separable Residue Extensions

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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20. Additional Invariants in the Case e x (X) = 2

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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21. Termination of the Fundamental Sequences of -Permissible Blow-Ups, and the Case e x (X) = 1

Author

Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Cossart, Vincent, Jannsen, Uwe, Saito, Shuji, and Schober, Bernd, With Contrib. by

Published
2020
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24. Resolution of Singularities of Arithmetical Threefolds II

Author

Cossart, Vincent and Piltant, Olivier

Subjects
Mathematics - Algebraic Geometry
Abstract

We prove Grothendieck's Conjecture on Resolution of Singulari-ties for quasi-excellent schemes X of dimension three and of arbitrary characteristic. This applies in particular to X = SpecA, A a reduced complete Noetherian local ring of dimension three and to algebraic or arithmetical varieties of dimension three. Similarly, if F is a number field, a complete discretely valued field or more generally the quotient field of any excellent Dedekind domain O, any regular projective sur-face X/F has a proper and flat model X over O which is everywhere regular., Comment: updates and extends 'Resolution of Singularities of Arithmetical Threefolds I' posted on this website

Published
2014

25. A strictly decreasing invariant for resolution of singularities in dimension two

Author

Cossart, Vincent and Schober, Bernd

Subjects
Mathematics - Algebraic Geometry
Abstract

We construct a local invariant for resolution of singularities of 2-dimensional excellent Noetherian schemes with boundary. We prove that the invariant strictly decreases at every step of the algorithm of Cossart, Jannsen and Saito., Comment: 41 pages, improved exposition, clarified minor details, added section of the termination of the CJS algorithm

Published
2014

26. Characteristic polyhedra of singularities without completion -- Part II

Author

Cossart, Vincent and Schober, Bernd

Subjects
Mathematics - Algebraic Geometry
Abstract

Hironaka's characteristic polyhedron is an important combinatorial object reflecting the local nature of a singularity. We prove that it can be determined without passing to the completion if the local ring is a G-ring and if additionally either it is Henselian, or a certain polynomiality condition $ (\mathrm{Pol}) $ holds, or a mild condition $(*) $ on the singularity holds. For example, the latter is fulfilled if the residue field is perfect., Comment: 46 pages; minor changes

Published
2014

29. Existence des diviseurs dicritiques, d'apr\`es S.S.Abhyankar

Author

Cossart, Vincent, Matusinski, Mickaël, and Moreno-Socias, Guillermo

Subjects
Mathematics - Algebraic Geometry
Abstract

In geometric terms, given a singular foliation of the plane, a dicritical divisor is (whenever it exists) an irreducible component of the exceptional divisor which is transverse to the foliation. Abhyankar gave recently a definition of the dicritical divisors which generalize and algebraicize the geometrical definition in the local case and the polynomial case. Following his work, we give a geometrical interpretation of these dicritical divisors and new proofs of their existence., Comment: 9 pages, in French

Published
2012
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30. Characteristic polyhedra of singularities without completion

Author

Cossart, Vincent and Piltant, Olivier

Subjects
Mathematics - Algebraic Geometry
Abstract

Let $(R,M,k)$ be a regular local G-ring with regular system of parameters $(u_1, \ldots ,u_d,y)$. We prove that the Hironaka characteristic polyhedron $\Delta (f;u_1, \ldots ,u_d)$, $f \not \in (u_1, \ldots ,u_d)$ of a hypersurface singularity $X={\rm Spec}R/(f)$ can be computed in some system of coordinates belonging to $R$. No assumption on the residue characteristic is required.

Published
2012

31. Dicritical divisors after S.S. Abhyankar et I. Luengo

Author

Cossart, Vincent and Matusinski, Mickaël

Subjects
Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry
Abstract

In [AL11], S.S Abhyankar and I. Luengo introduce a new theory of dicritical divisors in the most general framework. Here we simplify and generalize their results (see Theorems 3.1 and 3.2).

Published
2011
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32. Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes

Author

Cossart, Vincent, Jannsen, Uwe, and Saito, Shuji

Subjects
Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 14J17, 14E15
Abstract

We prove the existence of resolution of singularities for arbitrary (not necessarily reduced or irreducible) excellent two-dimensional schemes, via permissible blow-ups. The resolution is canonical, and functorial with respect to automorphisms or etale or Zariski localizations. We treat the embedded case as well as the non-embedded case, with or without a boundary, and we relate the diferent versions. In the non-embedded case, a boundary is a collection of locally principal closed subschemes. Our main tools are the stratifications by Hilbert-Samuel functions and the characteristic polyhedra introduced by H. Hironaka. In an appendix we show that the standard method used in characteristic zero - the theory of maximal contact - does not work for surfaces in positive characteristic (the counterexamples are hypersurfaces in affine threespace and work over any field of positive characteristic). In this new version, we treat the case of locally noetherian but not necessarily noetherian schemes in an appropriate way. Here one does not have a finite resolution sequence, but still a canonical resolution morphism by glueing. The same techniques allow to treat algebraic spaces and stacks., Comment: 169 pages, 3 figures

Published
2009

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