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Normal forms for rank two linear irregular differential equations and moduli spaces
- Source :
- Periodica Mathematica Hungarica, Periodica Mathematica Hungarica, 2022, 84, pp.303-320. ⟨10.1007/s10998-021-00408-8⟩, Periodica Mathematica Hungarica, Springer Verlag, In press, ⟨10.1007/s10998-021-00408-8⟩
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- International audience; We provide a unique normal form for rank two irregular connections on the Riemann sphere.In fact, we provide a birational model where we introduce apparent singular points and where the bundlehas a fixed Birkhoff-Grothendieck decomposition. The essential poles and the apparent poles provide twoparabolic structures. The first one only depend on the formal type of the singular points. The latter one determine the connection (accessory parameters). As a consequence, an open set of the corresponding moduli space of connections is canonically identified with an open set of some Hilbert scheme of points on the explicit blow-up of some Hirzebruch surface. This generalizes to the irregular case a description dueto Oblezin, and Saito-Szabo in the logarithmic case. This approach is also very close to the work of Dubrovin-Mazzocco with the cyclic vector.
- Subjects :
- Pure mathematics
Rank (linear algebra)
General Mathematics
Connection (vector bundle)
Open set
Riemann sphere
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
Type (model theory)
01 natural sciences
symbols.namesake
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
0103 physical sciences
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
0101 mathematics
Algebraic Geometry (math.AG)
Mathematics
010102 general mathematics
16. Peace & justice
Hirzebruch surface
Moduli space
Hilbert scheme
Mathematics - Classical Analysis and ODEs
symbols
010307 mathematical physics
Subjects
Details
- Language :
- English
- ISSN :
- 00315303 and 15882829
- Database :
- OpenAIRE
- Journal :
- Periodica Mathematica Hungarica, Periodica Mathematica Hungarica, 2022, 84, pp.303-320. ⟨10.1007/s10998-021-00408-8⟩, Periodica Mathematica Hungarica, Springer Verlag, In press, ⟨10.1007/s10998-021-00408-8⟩
- Accession number :
- edsair.doi.dedup.....1d86a929f61c970b6e1bad1390c908cd