Global nilpotent cones for twisted GL_r-Hitchin fibrations on curves and for moduli of 1D sheaves on K3 and other surfaces are nowhere reduced, with a criterion for primitive homology in Beauville-Mukai systems on K3 surfaces.
Le lemme fondamental pour les algèbres de Lie.Publ
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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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Non-reduced components of global nilpotent cones
Global nilpotent cones for twisted GL_r-Hitchin fibrations on curves and for moduli of 1D sheaves on K3 and other surfaces are nowhere reduced, with a criterion for primitive homology in Beauville-Mukai systems on K3 surfaces.
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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.