# Symplectic involutions on deformations of K3[2]

Open Mathematics (2012)

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

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topGiovanni 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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