Torsion Tate-Shafarevich twists of projective Lagrangian fibrations induce isomorphisms on rational cohomology that preserve Hodge structures and pairings, and the spaces are deformation-equivalent when the base is smooth and sections exist.
The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves
4 Pith papers cite this work. Polarity classification is still indexing.
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For rank-two bundles on genus-two hyperelliptic curves, the Chow ring of the universal moduli stack is tautological with explicit generators and relations.
Cohomology of compactified Jacobians is independent of degree and stability condition, shown by direct summation over strata.
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Topology of projective Tate-Shafarevich twists
Torsion Tate-Shafarevich twists of projective Lagrangian fibrations induce isomorphisms on rational cohomology that preserve Hodge structures and pairings, and the spaces are deformation-equivalent when the base is smooth and sections exist.
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Cycles in the universal moduli stack of bundles of rank two over genus two curves
For rank-two bundles on genus-two hyperelliptic curves, the Chow ring of the universal moduli stack is tautological with explicit generators and relations.
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Universal compactified Jacobians: cohomological invariance and boundary combinatorics
Cohomology of compactified Jacobians is independent of degree and stability condition, shown by direct summation over strata.
- Support theorem of universal compactified Jacobians