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arXiv · 2311.15697

The 3-fold K-theoretic DT/PT vertex correspondence holds

Nikolas Kuhn·Henry Liu·Felix Thimm
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Abstract

We prove the 3-fold DT/PT correspondence for K-theoretic vertices via wall-crossing techniques. We provide two different setups, following Mochizuki and following Joyce; both reduce the problem to q-combinatorial identities on word rearrangements. An important technical step is the construction of symmetric almost-perfect obstruction theories (APOTs) on auxiliary moduli stacks, e.g. master spaces, from the symmetric DT or PT obstruction theory. For this, we introduce symmetrized pullbacks of symmetric obstruction theories along smooth morphisms of Artin stacks.

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Nikolas Kuhn, Henry Liu, Felix Thimm. 2023-11-27. The 3-fold K-theoretic DT/PT vertex correspondence holds. https://doi.org/10.2140/gt.2026.30.71

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