Deformation of the O'Grady moduli spaces
| Autor: | Arvid Perego, Antonio Rapagnetta |
|---|---|
| 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: | 2013 |
| Předmět: |
Pure mathematics
General Mathematics Abelian surface Algebraic Geometry Moduli spaces of sheaves Deformation theory Hyperkahler manifolds K3 surfaces 01 natural sciences K3 surface symplectic resolutions Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics 0101 mathematics Abelian group Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Moduli spaces of sheaves Symplectic manifold Mathematics deformations Applied Mathematics 010102 general mathematics Moduli space Deformation theory Hyperkahler manifolds abelian surfaces Settore MAT/03 - Geometria 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Algebraic Geometry Symplectic geometry |
| Zdroj: | Journal für die reine und angewandte Mathematik Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2013, 678, pp.1--34. ⟨10.1515/CRELLE.2011.191⟩ |
| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/CRELLE.2011.191⟩ |
| Popis: | In this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If $S$ is a K3, $v=2w$ is a Mukai vector on $S$, where $w$ is primitive and $w^{2}=2$, and $H$ is a $v-$generic polarization on $S$, then the moduli space $M_{v}$ of $H-$semistable sheaves on $S$ whose Mukai vector is $v$ admits a symplectic resolution $\widetilde{M}_{v}$. A particular case is the $10-$dimensional O'Grady example $\widetilde{M}_{10}$ of irreducible symplectic manifold. We show that $\widetilde{M}_{v}$ is an irreducible symplectic manifold which is deformation equivalent to $\widetilde{M}_{10}$ and that $H^{2}(M_{v},\mathbb{Z})$ is Hodge isometric to the sublattice $v^{\perp}$ of the Mukai lattice of $S$. Similar results are shown when $S$ is an abelian surface. 29 pages |
| Databáze: | OpenAIRE |
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