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arXiv · 1908.01199

Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry

Hunter Dinkins·Andrey Smirnov
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Abstract

Let $X$ be a Nakajima quiver variety and $X'$ its $3d$-mirror. We consider the action of the Picard torus $\mathsf{K}=\mathrm{Pic}(X)\otimes \mathbb{C}^{\times}$ on $X'$. Assuming that $(X')^{\mathsf{K}}$ is finite, we propose a formula for the $\mathsf{K}$-character of the tangent spaces at the fixed points in terms of certain enumerative invariants of $X$ known as vertex functions.

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Hunter Dinkins, Andrey Smirnov. 2019-08-03. Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry. https://doi.org/10.1007/s11005-020-01292-y

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