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arXiv · 2102.08412

Discriminants and semi-orthogonal decompositions

Alex Kite·Ed Segal
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Abstract

The derived categories of toric varieties admit semi-orthogonal decompositions coming from wall-crossing in GIT. We prove that these decompositions satisfy a Jordan-Holder property: the subcategories that appear, and their multiplicities, are independent of the choices made. For Calabi-Yau toric varieties wall-crossing instead gives derived equivalences and autoequivalences, and mirror symmetry relates these to monodromy around the GKZ discriminant locus. We formulate a conjecture equating intersection multiplicities in the discriminant with the multiplicities appearing in certain semi-orthogonal decompositions. We then prove this conjecture in some cases.

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Alex Kite, Ed Segal. 2021-02-16. Discriminants and semi-orthogonal decompositions. https://doi.org/10.1007/s00220-021-04298-2

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