manuscripta mathematica

, Volume 72, Issue 1, pp 163–180

Birational properties of moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces

  • Zhenbo Qin

DOI: 10.1007/BF02568273

Cite this article as:
Qin, Z. Manuscripta Math (1991) 72: 163. doi:10.1007/BF02568273


LetX be a smooth algebraic surface over the complex number field. Fix a polarizationL, an invertible sheafc1 and an integerc2 such that (4c2-c12) is positive. letML(c1,c2) be the moduli space ofL-stable locally free rank-2 sheaves onX with chern classesc1 andc2 respectively, and let ξ be a numerical equivalence class defining a nonempty wall of type (c1,c2). We study the properties ofEξ(c1,c2) and obtain estimations for its dimension. Then, we discuss the existence of trivial polarizations, and determine the birational structures of moduli spacesML(c1,c2) whenX is a minimal surface of general type and (4c2-c12) is sufficiently large.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Zhenbo Qin
    • 1
  1. 1.Department of Mathematics and statisticsMcMaster UniversityHamiltonCanada