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

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.