Meachan, C. and Zhang, Z. (2016) Birational geometry of singular moduli spaces of O'Grady type. Advances in Mathematics, 296, pp. 210-267. (doi: 10.1016/j.aim.2016.02.036)
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Abstract
Following Bayer and Macrì, we study the birational geometry of singular moduli spaces M of sheaves on a K3 surface X which admit symplectic resolutions. More precisely, we use the Bayer–Macrì map from the space of Bridgeland stability conditions Stab(X) to the cone of movable divisors on M to relate wall-crossing in Stab(X) to birational transformations of M . We give a complete classification of walls in Stab(X) and show that every minimal birational model of M in the sense of the log minimal model program appears as a moduli space of Bridgeland semistable objects on X. An essential ingredient of our proof is an isometry between the orthogonal complement of a Mukai vector inside the algebraic Mukai lattice of X and the Néron–Severi lattice of M which generalises results of Yoshioka, as well as Perego and Rapagnetta. Moreover, this allows us to conclude that the symplectic resolution of M is deformation equivalent to the 10-dimensional irreducible holomorphic symplectic manifold found by O'Grady.
| Item Type: | Articles |
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| Additional Information: | C. M. is supported by an EPSRC Doctoral Prize Research Fellowship Grant EP/K503034/1 and Z. Z. is supported by an EPSRC Standard Research Grant EP/J019410/1. We also appreciate the support from the University of Bonn, the Max Planck Institute for Mathematics, and the SFB/TR-45 during the initial stage of this project as well as the Hausdorff Research Institute for Mathematics for its conclusion. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Meachan, Dr Ciaran |
| Authors: | Meachan, C., and Zhang, Z. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Advances in Mathematics |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| Published Online: | 18 April 2016 |
| Copyright Holders: | Copyright © 2016 Elsevier Inc. |
| First Published: | First published in Advances in Mathematics 296: 210-267 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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