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Birational models of
moduli spaces of coherent sheaves on the projective plane
Chunyi Li and Xiaolei Zhao |
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Geometry & Topology 23 (2019) 347–426
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Abstract |
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We study the birational geometry of moduli spaces of semistable sheaves on the projective plane via Bridgeland stability conditions. We show that the entire MMP of their moduli spaces can be run via wall-crossing. Via a description of the walls, we give a numerical description of their movable cones, along with its chamber decomposition corresponding to minimal models. As an application, we show that for primitive vectors, all birational models corresponding to open chambers in the movable cone are smooth and irreducible. |
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Keywords
birational geometry, moduli space of sheaves, stability
condition, wall-crossing
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Mathematical Subject Classification 2010
Primary: 14D20
Secondary: 14E30
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References |
Publication
Received: 28 July 2017
Revised: 29 March 2018
Accepted: 11 May 2018
Published: 5 March 2019
Proposed: Richard Thomas
Seconded: Dan Abramovich, Jim Bryan
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Authors |
| Chunyi Li | |
| School of Mathematics The University of Edinburgh Edinburgh United Kingdom |
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| Xiaolei Zhao | |
| Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
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