Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
O'Grady, Desingularized moduli spaces of sheaves on a K3 , J
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Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
Extends classification of rank-2 co-Higgs bundles on Hopf surfaces to construct Poisson 3-folds and describe their symplectic leaves.
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A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
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Finite order symplectic birational self-maps on Kummer-type manifolds
Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
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Terminalizations of quotients of compact hyperk\"ahler manifolds by induced symplectic automorphisms
Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
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Poisson three-folds constructed from co-Higgs bundles on Hopf surfaces
Extends classification of rank-2 co-Higgs bundles on Hopf surfaces to construct Poisson 3-folds and describe their symplectic leaves.