Tautological stable pair invariants of Calabi-Yau 4-folds

Abstract

Let $X$ be a Calabi-Yau 4-fold and $D$ a smooth divisor on it. We consider tautological complex associated with $L={\mathcal{O}}_X(D)$ on the moduli space of Le Potier stable pairs and define its counting invariant by integrating the Euler class against the virtual class. We conjecture a formula for their generating series expressed using genus zero Gopakumar-Vafa invariants of $D$ and genus one Gopakumar-Vafa type invariants of $X$, which we verify in several examples. When $X$ is the local resolved conifold, our conjecture reproduces a conjectural formula of Cao-Kool-Monavari in the PT chamber. In the JS chamber, we completely determine the invariants and confirm one of our previous conjectures.

26 pages. Published version

References in corpus (4)

• Enumerative geometry of 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
• Counting perverse coherent systems on Calabi-Yau 4-folds

Cited by in corpus (7)

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• Enumerative invariants and wall-crossing formulae in abelian categories
• Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds