Fibrés stables et fibrés exceptionnels sur \({\mathbb{P}}_ 2\). (Stable sheaves and exceptional sheaves over \({\mathbb{P}}_ 2)\). (French) Zbl 0586.14007
In this interesting paper, the authors show for which r, \(c_ 1, c_ 2\), there is a rank r stable vector bundle on \({\mathbb{P}}^ 2\) with Chern classes \(c_ 1, c_ 2\). Furthermore they give a construction of the moduli space of torsion-free semi-stable sheaves with given rank and Chern classes and show its irreducibility. A crucial step for the proofs is the study of stable vector bundles with \(Ext^ 1(E,E)=0\) (i.e. rigid): they call them exceptional bundles. For more on these bundles, see J. M. Drezet [Math. Ann. 275, 25-48 (1986; Zbl 0578.14013)].
Reviewer: E.Ballico
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
| 32G13 | Complex-analytic moduli problems |
| 14D22 | Fine and coarse moduli spaces |
Keywords:
flag; filtration; rigidity; rank r stable vector bundle; Chern classes; moduli space of torsion-free semi-stable sheaves; exceptional bundlesCitations:
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