Donaldson-Thomas invariants of [\mathbb C⁴/\mathbb Z_r]

2025/07/29 by Liu, Xiaolong
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2507.21582

Abstract

We compute the zero-dimensional Donaldson-Thomas invariants of the quotient stack [ℂ⁴/ℤ_r], confirming a conjecture of Cao-Kool-Monavari. Our main theorem is established through an orbifold analogue of Cao-Zhao-Zhou's degeneration formula combined with the zero-dimensional Donaldson-Thomas invariants for A_r-1×ℂ² and an explicit determination of orientations of Hilbert schemes of points on [ℂ⁴/ℤ_r].

Citations

• Cosection localization via shifted symplectic geometry
• Bordism categories and orientations of moduli spaces
• K-theoretic pullbacks for Lagrangians on derived critical loci
• Shifted symplectic pushforwards
• Quasimaps to quivers with potentials
• Complex Kuranishi structures and counting sheaves on Calabi-Yau 4-folds, II
• Instanton Counting and Donaldson-Thomas Theory on Toric Calabi-Yau Four-Orbifolds
• Counting surfaces on Calabi-Yau 4-folds I: Foundations
• Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds
• Counting sheaves on Calabi-Yau 4-folds, I
• Orientations for DT invariants on quasi-projective Calabi-Yau 4-folds
• Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli of\n objects
• Topological Hochschild homology and integral p-adic Hodge theory
• Lectures on K-theoretic computations in enumerative geometry
• Derived Algebraic Geometry
• Shifted Symplectic Structures
• Good degeneration of Quot-schemes and coherent systems
• Virtual pull-backs
• Algebraic cobordism revisited
• The local Donaldson-Thomas theory of curves
• Gromov-Witten theory and Donaldson-Thomas theory, II
• Gromov-Witten theory and Donaldson-Thomas theory, I
• Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

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• Donaldson-Thomas invariants of Calabi-Yau orbifolds under flops
• On a computation of rank two Donaldson-Thomas invariants
• Donaldson-Thomas theory for Calabi-Yau 4-folds