, Volume 72, Issue 1, pp 163-180

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

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Abstract

LetX be a smooth algebraic surface over the complex number field. Fix a polarizationL, an invertible sheafc 1 and an integerc 2 such that (4c 2-c 1 2 ) is positive. letM L(c 1,c 2) be the moduli space ofL-stable locally free rank-2 sheaves onX with chern classesc 1 andc 2 respectively, and let ξ be a numerical equivalence class defining a nonempty wall of type (c 1,c 2). We study the properties ofE ξ(c 1,c 2) and obtain estimations for its dimension. Then, we discuss the existence of trivial polarizations, and determine the birational structures of moduli spacesM L(c 1,c 2) whenX is a minimal surface of general type and (4c 2-c 1 2 ) is sufficiently large.