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arXiv · 2006.14695

Quasimaps and stable pairs

Henry Liu
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Abstract

We prove an equivalence between the Bryan--Steinberg theory of $\pi$-stable pairs on $Y = \mathcal{A}_{m-1} \times \mathbb{C}$ and the theory of quasimaps to $X = \mathrm{Hilb}(\mathcal{A}_{m-1})$, in the form of an equality of K-theoretic equivariant vertices. In particular, the combinatorics of both vertices are described explicitly via box counting. Then we apply the equivalence to study the implications for sheaf-counting theories on $Y$ arising from 3d mirror symmetry for quasimaps to $X$, including the Donaldson--Thomas crepant resolution conjecture.

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Henry Liu. 2020-06-25. Quasimaps and stable pairs. https://doi.org/10.1017/fms.2021.25

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