Perverse sheaves of categories and some applications

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 P1 bundles, semiorthogonal decompositions, and relate them to a recent proof of Segal that all autoequivale...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2019-08, Vol.352, p.1155-1205
Main Authors: Harder, Andrew, Katzarkov, Ludmil
Format: Article
Language:English
Subjects:
Degenerations of K3 surfaces
Derived categories
Homological mirror symmetry
Perverse sheaves
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Summary: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 P1 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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2019.05.024