| Title: |
Factoriality Properties of Moduli Spaces of Sheaves on Abelian and K3 Surfaces |
| Authors: |
Perego, Arvid; Rapagnetta, Antonio |
| Contributors: |
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, Italia = University of Rome Tor Vergata Rome, Italy = Université de Rome Tor Vergata Rome, Italie |
| Source: |
ISSN: 1073-7928. |
| Publisher Information: |
CCSD; Oxford University Press (OUP) |
| Publication Year: |
2012 |
| Collection: |
Université de Lorraine: HAL |
| Subject Terms: |
factoriality; abelian surfaces; K3 surfaces; Moduli spaces of sheaves; [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] |
| Description: |
International audience ; 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 MvpS, Hq 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 MvpS, Hq (when S is K3) and of the fiber KvpS, Hq of the Albanese map of MvpS, Hq (when S is abelian). Then, if S is K3 we show that MvpS, Hq is either locally factorial or 2´factorial, and we give an example of both cases. If S is abelian, we show that MvpS, Hq and KvpS, Hq are 2´factorial. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/1103.3957; ARXIV: 1103.3957 |
| DOI: |
10.1093/imrn/rns233 |
| Availability: |
https://hal.science/hal-01266784; https://hal.science/hal-01266784v1/document; https://hal.science/hal-01266784v1/file/Factoriality_11-2011-arxiv.pdf; https://doi.org/10.1093/imrn/rns233 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.E3D514FD |
| Database: |
BASE |