Symplectic involutions on deformations of K3[2]

Giovanni Mongardi

Open Mathematics (2012)

  • Volume: 10, Issue: 4, page 1472-1485
  • ISSN: 2391-5455

Abstract

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Let X be a hyperkähler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H 2(X, ℤ) is isomorphic to E 8(−2). Finally we show that any couple consisting of one such manifold and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a symplectic involution on the K3 surface.

How to cite

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Giovanni Mongardi. "Symplectic involutions on deformations of K3[2]." Open Mathematics 10.4 (2012): 1472-1485. <http://eudml.org/doc/269387>.

@article{GiovanniMongardi2012,
abstract = {Let X be a hyperkähler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H 2(X, ℤ) is isomorphic to E 8(−2). Finally we show that any couple consisting of one such manifold and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a symplectic involution on the K3 surface.},
author = {Giovanni Mongardi},
journal = {Open Mathematics},
keywords = {Symplectic involution; Holomorphic symplectic fourfolds; holomorphic symplectic fourfolds; symplectic involution},
language = {eng},
number = {4},
pages = {1472-1485},
title = {Symplectic involutions on deformations of K3[2]},
url = {http://eudml.org/doc/269387},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Giovanni Mongardi
TI - Symplectic involutions on deformations of K3[2]
JO - Open Mathematics
PY - 2012
VL - 10
IS - 4
SP - 1472
EP - 1485
AB - Let X be a hyperkähler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H 2(X, ℤ) is isomorphic to E 8(−2). Finally we show that any couple consisting of one such manifold and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a symplectic involution on the K3 surface.
LA - eng
KW - Symplectic involution; Holomorphic symplectic fourfolds; holomorphic symplectic fourfolds; symplectic involution
UR - http://eudml.org/doc/269387
ER -

References

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