Proves existence of virtual fundamental class on KSBA moduli space of stable general type surfaces by constructing it on the moduli stack of lci covers and pushing forward.
Grothendieck Duality for Deligne-Mumford Stacks
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to its coarse moduli space and on representable morphisms. We explicitly compute the dualizing complex for a smooth stack over an algebraically closed field and prove that Serre duality holds for smooth compact Deligne-Mumford stacks in its usual form. We prove also that a proper Cohen-Macaulay stack has a dualizing sheaf and it is an invertible sheaf when it is Gorenstein. As an application of this general machinery we compute the dualizing sheaf of a tame nodal curve.
verdicts
UNVERDICTED 4representative citing papers
Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
The dissertation rewrites positive Schubert geometry via spectral algebraic geometry and differential cohesion to construct a categorical dual to the Amplituhedron with a De Rham volume.
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
citing papers explorer
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The virtual fundamental class for the moduli space of surfaces of general type
Proves existence of virtual fundamental class on KSBA moduli space of stable general type surfaces by constructing it on the moduli stack of lci covers and pushing forward.
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Functoriality of logarithmic Hochschild homology of log smooth pairs
Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
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Brave new categorical spectral positive Schubert geometry and the categorical Dual Amplituhedron
The dissertation rewrites positive Schubert geometry via spectral algebraic geometry and differential cohesion to construct a categorical dual to the Amplituhedron with a De Rham volume.
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Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.