Factoriality Properties of Moduli Spaces of Sheaves on Abelian and K3 Surfaces
| Autor: | Antonio Rapagnetta, Arvid Perego |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Roma Tor Vergata [Roma] |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
Factorial General Mathematics Algebraic Geometry Moduli spaces of sheaves K3 surfaces Abelian surfaces K3 surfaces 01 natural sciences K3 surface Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics 0101 mathematics Abelian group Algebraic Geometry (math.AG) Moduli spaces of sheaves Mathematics 010102 general mathematics Moduli space Algebra abelian surfaces Physics::Accelerator Physics factoriality Settore MAT/03 - Geometria 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Algebraic Geometry |
| Zdroj: | International Mathematics Research Notices International Mathematics Research Notices, Oxford University Press (OUP), 2012, 2014 (3), pp.643--680. ⟨10.1093/imrn/rns233⟩ |
| ISSN: | 1073-7928 1687-0247 |
| DOI: | 10.1093/imrn/rns233⟩ |
| Popis: | In this paper we complete the determination of the index of factoriality of moduli spaces of semistable sheaves on an abelian or projective K3 surface $S$. If $v=2w$ is a Mukai vector, $w$ is primitive, $w^{2}=2$ and $H$ is a generic polarization, let $M_{v}(S,H)$ be the moduli space of $H-$semistable sheaves on $S$ with Mukai vector $v$. First, we describe in terms of $v$ the pure weight-two Hodge structure and the Beauville form on the second integral cohomology of the symplectic resolutions of $M_{v}(S,H)$ (when $S$ is K3) and of the fiber $K_{v}(S,H)$ of the Albanese map of $M_{v}(S,H)$ (when $S$ is abelian). Then, if $S$ is K3 we show that $M_{v}(S,H)$ is either locally factorial or $2-$factorial, and we give an example of both cases. If $S$ is abelian, we show that $M_{v}(S,H)$ and $K_{v}(S,H)$ are $2-$factorial. 14 pages; added calculation of the weight-two Hodge structures of the symplectic resolutions, bibliographical references corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|