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Globally generated vector bundles with small c1 on projective spaces, II.
- Source :
-
Mathematische Nachrichten . Nov2022, Vol. 295 Issue 11, p2071-2103. 33p. - Publication Year :
- 2022
-
Abstract
- We complete the classification of globally generated vector bundles with c1≤5$c_1 \le 5$ on projective spaces by treating the case c1=5$c_1 = 5$ on Pn$\mathbb {P}^n$, n≥4$n \ge 4$. It turns out that there are very few indecomposable bundles of this kind: besides some obvious examples there are, roughly speaking, only the (first twist of the) rank 5 vector bundle which is the middle term of the monad defining the Horrocks bundle of rank 3 on P5$\mathbb {P}^5$, and its restriction to P4$\mathbb {P}^4$. We recall, in an appendix, from one of our previous papers, the main results allowing the classification of globally generated vector bundles with c1=5$c_1 = 5$ on P3$\mathbb {P}^3$. Since there are many such bundles, a large part of the main body of the paper is occupied with the proof of the fact that, except for the simplest ones, they do not extend to P4$\mathbb {P}^4$ as globally generated vector bundles. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PROJECTIVE spaces
*VECTOR bundles
Subjects
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 295
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 160509112
- Full Text :
- https://doi.org/10.1002/mana.202000093