Derived Categories of Toric Varieties

摘要

The purpose of this paper is to investigate the structure of the derived category of a toric variety. We shall prove the following result. Theorem 1.1. Let X be a protective toric variety with at most quotient singularities, let B be an invariant Q-divisor whose coefficients belong to the set {(r-1)/r; r ∈ Z_( >0 )}, and let X be the smooth Deligne-Mumford stack associated to the pair (X, B) as in [12]. Then the bounded derived category of coherent sheaves D~b(Coh(X)) has a complete exceptional collection consisting of sheaves.