# Quasimaps and stable pairs

@article{Liu2021QuasimapsAS,
title={Quasimaps and stable pairs},
author={H. Liu},
journal={Forum of Mathematics, Sigma},
year={2021},
volume={9}
}
• H. Liu
• Published 2021
• Mathematics, Physics
• Forum of Mathematics, Sigma
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 $X = \text{Hilb}(\mathcal {A}_{m-1})$, 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… Expand
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