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- Title
Brill-Noether theory for moduli spaces of sheaves on algebraic varieties.
- Authors
Costa, Laura; Miró-Roig, Rosa Maria
- Abstract
Let X be a smooth projective variety of dimension n and let H be an ample line bundle on X. Let MX,H( r; c1, . . . , cs) be the moduli space of H-stable vector bundles E on X of rank r and Chern classes ci( E) = ci for i = 1, . . . , s ≔ min{ r, n}. We define the Brill-Noether filtration on MX,H ( r; c1, . . . , cs) as and we realize as the kth determinantal variety of a morphism of vector bundles on MX,H( r; c1, . . . , cs), provided Hi( E) = 0 for i ≥ 2 and E ∈ MX,H ( r; c1, . . . , cs). We also compute the expected dimension of . Very surprisingly we will see that the Brill-Noether stratification allow us to compare moduli spaces of vector bundles on Hirzebruch surfaces stables with respect to different polarizations. We will also study the Brill-Noether loci of the moduli space of instanton bundles and we will see that they have the expected dimension.
- Subjects
GENERALIZED spaces; VECTOR bundles; MODULES (Algebra); SET theory; MORPHISMS (Mathematics)
- Publication
Forum Mathematicum, 2010, Vol 22, Issue 3, p411
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/FORUM.2010.023