| Title: |
Moduli spaces of bundles over non-projective K3 surfaces |
| Authors: |
Perego, Arvid; Toma, Matei |
| Contributors: |
Institut Élie Cartan de Lorraine (IECL); Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) |
| Source: |
https://hal.science/hal-01269780 ; 2016. |
| Publisher Information: |
CCSD |
| Publication Year: |
2016 |
| Collection: |
Université de Lorraine: HAL |
| Subject Terms: |
moduli spaces of sheaves; twisted sheaves; K3 surfaces; [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]; [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] |
| Description: |
We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if v = (r, ξ, a) is a Mukai vector on a K3 surface S with r prime to ξ and ω is a " generic " Kähler class on S, we show that the moduli space M of µ ω −stable sheaves on S with associated Mukai vector v is an irreducible holo-morphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. If M parametrizes only locally free sheaves, it is moreover hyperkähler. Finally, we show that there is an isometry between v ⊥ and H 2 (M, Z) and that M is projective if and only if S is projective. |
| Document Type: |
report |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/1403.0104; ARXIV: 1403.0104 |
| Availability: |
https://hal.science/hal-01269780; https://hal.science/hal-01269780v1/document; https://hal.science/hal-01269780v1/file/20160204arxiv.pdf |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.158A0EF4 |
| Database: |
BASE |