Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
Equivalences between GIT quotients of Landau-Ginzburg B-models
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.
fields
math.AG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves equivalence of derived category of branched double cover to matrix factorizations for fiberwise quadratic potential on line bundle with odd-degree fiber coordinate and non-split grading.
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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
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Odd Kn\"orrer periodicity as a double cover
Proves equivalence of derived category of branched double cover to matrix factorizations for fiberwise quadratic potential on line bundle with odd-degree fiber coordinate and non-split grading.