Donaldson-Thomas theory of quantum Fermat quintic threefolds I

Abstract

In this paper, we study non-commutative projective schemes whose associated non-commutative graded algebras are finite over their centers. We study their moduli spaces of stable sheaves, and construct a symmetric obstruction theory in the Calabi-Yau-3 case. This allows us to define Donaldson-Thomas type invariants. We also discuss the simplest examples, called quantum Fermat quintic threefolds.

arXiv comment22 pages. Fix some typos, move some results to the sequel, and reorganize the paper. Comments are welcome