Geometry of moduli space of sheaves on del Pezzo surfaces via Maruyama transform

Abstract

In this paper, we prove that the moduli space of stable pairs (or sheaves) on del Pezzo surface S is isomorphic to the Maruyama type transformation of a projective bundle of a quiver representation space.

Keywords:

• Birational geometry
• del Pezzo surface
• elementary modification
• stable sheaf

2010 Mathematics Subject Classification:

• 14C15
• 14E30
• 14N35

Additional information

Funding

Kiryong Chung is partially supported by Korea NRF grant 2016R1D1A1B03930. Jinwon Choi was supported by the Sookmyung Women’s University Research Grants (1-1603-2040) and NRF-2015R1C1A1A01054185.