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arXiv · 1708.01181

Perverse sheaves of categories and some applications

Andrew Harder·Ludmil Katzarkov
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Abstract

We study perverse sheaves of categories their connections to classical algebraic geometry. We show how perverse sheaves of categories encode naturally derived categories of coherent sheaves on $\mathbb{P}^1$ bundles, semiorthogonal decompositions, and relate them to a recent proof of Segal that all autoequivalences of triangulated categories are spherical twists. Furthermore, we show that perverse sheaves of categories can be used to represent certain degenerate Calabi--Yau varieties.

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Andrew Harder, Ludmil Katzarkov. 2017-08-03. Perverse sheaves of categories and some applications. https://doi.org/10.1016/j.aim.2019.05.024

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