A Categorical sl_2 Action on Some Moduli Spaces of Sheaves

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Date

2020-09-24

Authors

Takahashi, Ryan

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University of Oregon

Abstract

We study a certain sequence of moduli spaces of stable sheaves on a K3 surface of Picard rank 1 over $\mathbb{C}$. We prove that this sequence can be given the structure of a geometric categorical $\mathfrak{sl}_2$ action, a global version of an action studied by Cautis, Kamnitzer, and Licata. As a corollary, we find that the moduli spaces in this sequence which are birational are also derived equivalent.

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