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Birational models of moduli spaces of coherent sheaves on the projective plane

Chunyi Li and Xiaolei Zhao

Geometry & Topology 23 (2019) 347–426
Abstract

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.

Keywords
birational geometry, moduli space of sheaves, stability condition, wall-crossing
Mathematical Subject Classification 2010
Primary: 14D20
Secondary: 14E30
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
Authors
Chunyi Li
School of Mathematics
The University of Edinburgh
Edinburgh
United Kingdom
Xiaolei Zhao
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA
United States