Donaldson-Thomas theory of quantum Fermat quintic threefolds I
Yu-Hsiang Liu
TL;DR
This paper develops Donaldson-Thomas invariants for non-commutative Calabi-Yau threefolds, specifically quantum Fermat quintic threefolds, by constructing moduli spaces and symmetric obstruction theories.
Contribution
It introduces a framework for defining Donaldson-Thomas invariants in non-commutative settings, focusing on quantum Fermat quintic threefolds, a novel class of examples.
Findings
Construction of moduli spaces of stable sheaves on non-commutative schemes
Development of symmetric obstruction theory in the Calabi-Yau-3 case
Definition of Donaldson-Thomas type invariants for quantum Fermat quintic threefolds
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology