Counting perverse coherent systems on Calabi-Yau 4-folds

Abstract

Nagao-Nakajima introduced counting invariants of stable perverse coherent systems on small resolutions of Calabi-Yau 3-folds and determined them on the resolved conifold. Their invariants recover DT/PT invariants and Szendröi's non-commutative invariants in some chambers of stability conditions. In this paper, we study an analogue of their work on Calabi-Yau 4-folds. We define counting invariants for stable perverse coherent systems using primary insertions and compute them in all chambers of stability conditions. We also study counting invariants of local resolved conifold ${\mathcal{O}}_{{\mathbb{P}}^1}(-1,-1,0)$ defined using torus localization and tautological insertions. We conjecture a wall-crossing formula for them, which upon dimensional reduction recovers Nagao-Nakajima's wall-crossing formula on resolved conifold.

arXiv comment32 pages. Published version

References in corpus (19)

• The intrinsic normal cone
• Semiorthogonal decomposition for algebraic varieties
• Curve counting via stable pairs in the derived category
• Non-commutative Donaldson-Thomas theory and the conifold
• Enumerative geometry of Calabi-Yau 4-folds
• Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
• Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds
• Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Donaldson-Thomas theory for Calabi-Yau 4-folds
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Orientability for gauge theories on Calabi-Yau manifolds
• Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds

Cited by in corpus (6)

• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Categorical wall-crossing formula for Donaldson-Thomas theory on the resolved conifold
• Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds