Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.
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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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Hecke operators on symplectic surfaces and $\chi$-independence
Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.
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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.