Varieties of Complexes of Fixed Rank

Abstract

We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair of morphisms which are smooth with irreducible fibres.Keywords and phrases: complexes projective varieties, algebra of global dimension at most two, homologies of complexes, smooth morphisms.