Curve counting via stable objects in derived categories of Calabi-Yau 4-folds

Abstract

In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa (GV) type formula for the generating series of stable pair invariants on Calabi-Yau (CY) 4-folds. The purpose of this paper is to give an interpretation of the above GV type formula in terms of wall-crossing phenomena in the derived category. We introduce invariants counting LePotier's stable pairs on CY 4-folds, and show that they count certain stable objects in D0-D2-D8 bound states in the derived category. We propose a conjectural wall-crossing formula for the generating series of our invariants, which recovers the conjectural GV type formula. Examples are computed for both compact and toric cases to support our conjecture.

34 pages. Published version

References in corpus (10)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Enumerative geometry 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
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
• Stable pair invariants of local Calabi-Yau 4-folds
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Counting perverse coherent systems on Calabi-Yau 4-folds

Cited by in corpus (10)

• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Counting sheaves on Calabi-Yau 4-folds, I
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Counting perverse coherent systems on Calabi-Yau 4-folds
• Enumerative invariants and wall-crossing formulae in abelian categories
• Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• Cosection Localization and Vanishing for Virtual Fundamental Classes of D-Manifolds
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds