Moduli stacks of semistable sheaves and representations of Ext-quivers

Abstract

We show that the moduli stacks of semistable sheaves on smooth projective varieties are analytic locally on their coarse moduli spaces described in terms of representations of the associated Ext-quivers with convergent relations. When the underlying variety is a Calabi-Yau 3-fold, our result describes the above moduli stacks as critical locus analytic locally on the coarse moduli spaces. The results in this paper will be applied to the wall-crossing formula of Gopakumar-Vafa invariants defined by Maulik and the author.

52 pages, to appear in Geometry & Topology

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Homotopy L-infinity spaces
• Gopakumar-Vafa invariants and wall-crossing

Cited by in corpus (14)

• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• K-theoretic Hall algebras for quivers with potential
• Formality conjecture for K3 surfaces
• Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds
• Gopakumar-Vafa invariants and wall-crossing
• Refined invariants of finite-dimensional Jacobi algebras
• Purity and 2-Calabi-Yau categories
• Non-commutative deformations of simple objects in a category of perverse coherent sheaves
• Generators for categorical Hall algebras of surfaces
• On non-commutative formal deformations of coherent sheaves on an algebraic variety
• Affinizations of Lorentzian Kac-Moody Algebras and Hilbert Schemes of Points on K3 Surfaces
• Quivers with analytic potentials
• The categorical DT/PT correspondence and quasi-BPS categories for local surfaces
• On window theorem for categorical Donaldson-Thomas theories on local surfaces and its applications