Antisymplectic involutions of holomorphic symplectic manifolds
By A. Beauville. 2010
56 citations recorded by the source corpus.
Let X be a holomorphic symplectic manifold, of dimension divisible by four, and σ be an antisymplectic involution of X. The fixed locus F of σ is a Lagrangian submanifold of X; we show that its Â‐genus is one. As an application, we determine all possibilities for the Chern numbers of F when X is a deformation of the Hilbert square of a K3 surface.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cab171e47d9f84066894b96963e76cd729a38952
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In Geometry and Topology
Citations in the corpus
- A note on automorphisms and birational transformations of holomorphic symplectic manifolds (2009, methodology): “We refer to Beauville [3, 4], Boissière–Nieper-Wißkirchen– Sarti [8], Camere [12], O’Grady [26] and Oguiso–Schröer [31] for some constructions concerning Hilbert schemes of two points on K3 surfaces, generalized Kummer varieties, Fano varieties of lines on cubic fourfolds, double covers of EPW sexti”
- Symplectic involutions of holomorphic symplectic four‐folds (2010, background): “Many authors have studied the problem from different viewpoints; here we want to mention only the papers by Boissière [6] and Boissière– Sarti [7] on natural involutions and the paper by Beauville [4] in which he deals with the case of antisymplectic involutions.”
- Symplectic involutions on deformations of K3[2] (2011, methodology): “We remark that the isometry class of H2(X,Z) with the BeauvilleBogomolov form is invariant under smooth deformations.”