Involutions and linear systems on holomorphic symplectic manifolds
By Kieran G. O’Grady. 2004
77 citations recorded by the source corpus.
Abstract.A K3 surface with an ample divisor of self-intersection 2 is a double cover of the plane branched over a sextic curve. We conjecture that similar statement holds for the generic couple (X, H) with X a deformation of (K3)[n] and H an ample divisor of square 2 for Beauville’s quadratic form. If n = 2 then according to the conjecture X is a double cover of a singular) sextic 4-fold in $$\mathbb{P}^{5} .$$ It follows from the conjecture that a deformation of (K3)[n] carrying a divisor (not necessarily ample) of degree 2 has an anti-symplectic birational involution. We test the conjecture. In doing so we bump into some interesting geometry: examples of two antisymplectic involutions generating an interesting dynamical system, a case Strange duality and what is probably an involution on the moduli space degree-2 quasi-polarized (X, H) where X is a deformation of (K3)[2].
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/35cd9509305ae29a01de28a142293c07cb125004
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In Geometry and Topology
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Citations in the corpus
- Symplectic involutions on deformations of K3[2] (2011, background): “The papers [19, 20] by O’Grady study DoubleEPW sextics which are naturally endowed with an antisymplectic involution.”
- Automorphism groups of Calabi-Yau manifolds of Picard number two (2012, background): “X) is the Picard number of X. There are many interesting Calabi-Yau manifolds of Picard number 2 (for instance, [PSS71], [We88], [GP01], [Ku03], [Ku04] [Ca07], [Sc11], [OS01], [HT01], [HT09], [Yo01], [Ogr05], [Sa07]). We denote by (xn) X, where dim X = n, the top interesection form on Pic(X). As usu”
- Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics (2005, unknown): “A G ] 1 9”
- Double covers of EPW-sextics (2010, unknown): “16) of [12]) that gOP5(1) ∼= μ(D)−∆ [2] S .”