Involutions and linear systems on holomorphic symplectic manifolds |
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Authors: | K G O’Grady |
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Institution: | (1) Dipartimento di Matematica “Guido Castelnuovo”, Università di Roma “La Sapienza”, Piazzale Aldo Moro n. 5, 00185 Rome, Italy |
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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
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].
Received: June 2004 Revision: December 2004 Accepted: January 2005 |
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