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- W4300304003 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 describe the complementary components. We also 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 Orlov's $sigma$-model/Landau-Ginzburg model correspondence." @default.
- W4300304003 created "2022-10-03" @default.
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- W4300304003 date "2012-03-29" @default.
- W4300304003 modified "2023-09-25" @default.
- W4300304003 title "Variation of geometric invariant theory quotients and derived categories" @default.
- W4300304003 doi "https://doi.org/10.48550/arxiv.1203.6643" @default.
- W4300304003 hasPublicationYear "2012" @default.
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