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arXiv · 2507.05922

Wall-crossing for Calabi-Yau fourfolds: framework, tools, and applications

Arkadij Bojko
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Abstract

This work develops new ideas and tools to establish equivariant wall-crossing in Calabi-Yau four categories. In the process, I introduce several necessary formalisms, including an equivariant deformation of Joyce's vertex algebras built on a novel and explicitly computable definition of equivariant homology for stacks. The proof of the wall-crossing formula is then given for Calabi-Yau four quivers and local CY fourfolds. A crucial part of the problem is showing that the generalized invariants counting stable objects are well-defined. Using a conceptual argument akin to the quantum Lefschetz principle, I show that for torsion-free sheaves, this follows from the wall-crossing formula for Joyce-Song stable pairs. In joint work with Kuhn-Liu-Thimm, these frameworks together with functoriality established here for Park's virtual pullback diagrams are used to prove the general CY4 wall-crossing conjecture.

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Arkadij Bojko. 2025-07-08. Wall-crossing for Calabi-Yau fourfolds: framework, tools, and applications. https://arxiv.org/abs/2507.05922

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