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.
Proves Lagrangian correspondences in nonabelian Hodge theory for perfect complexes and establishes canonical shifted pretwistor structures on the Deligne-Hitchin-Simpson moduli stack over P^1_C.
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.