Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants

Abstract

We show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are proper algebraic stacks of finite type, if they satisfy the Bogomolov-Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson-Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi-Yau 3-folds satisfying the BG inequality conjecture, for example on étale quotients of abelian 3-folds.

Revised following referee comments, 44 pages, to appear in Crelle Journal

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Donaldson-Thomas invariants via microlocal geometry
• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Derived category of coherent sheaves and counting invariants

Cited by in corpus (8)

• Existence of moduli spaces for algebraic stacks
• Riemann-Hilbert problems from Donaldson-Thomas theory
• Hall algebras in the derived category and higher rank DT invariants
• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• Stability conditions on threefolds with nef tangent bundles
• Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds
• Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds
• Hilbert scheme of twisted cubics as simple wall-crossing