Variation of geometric invariant theory quotients and derived categories

Matthew Ballard, David Favero, Ludmil Katzarkov

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

We study the relationship between derived categories of factorizations on gauged Landau-Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived categories are comparable by semi-orthogonal decompositions and we completely describe all components appearing in these semi-orthogonal decompositions. We show how this general framework encompasses many well-known semi-orthogonal decompositions. We then proceed to give applications of this complete description.

In this setting, we verify a question posed by Kawamata: we show that D-equivalence and K-equivalence coincide for such variations. The results are applied to obtain a simple inductive description of derived categories of coherent sheaves on projective toric Deligne-Mumford stacks. This recovers Kawamata's theorem that all projective toric Deligne-Mumford stacks have full exceptional collections. Using similar methods, we prove that the Hassett moduli spaces of stable symmetrically-weighted rational curves also possess full exceptional collections. As a final application, we show how our results recover and extend Orlov's sigma-model/Landau-Ginzburg model correspondence.

OriginalspracheEnglisch
Seiten (von - bis)235–303
Seitenumfang69
FachzeitschriftJournal für die Reine und Angewandte Mathematik: Crelle's journal
Jahrgang2019
Ausgabenummer746
Frühes Online-Datum13 Feb. 2016
DOIs
PublikationsstatusVeröffentlicht - Jan. 2019

ÖFOS 2012

  • 101001 Algebra

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