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

Li, Chunyi¹ ; Zhao, Xiaolei²

¹ School of Mathematics, The University of Edinburgh, Edinburgh, United Kingdom
² Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States

Geometry & topology, Tome 23 (2019) no. 1, pp. 347-426.

Résumé

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.

Détail

DOI : 10.2140/gt.2019.23.347

Classification : 14D20, 14E30
Keywords: birational geometry, moduli space of sheaves, stability condition, wall-crossing

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