We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the 11-dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on Morrison-Nikulin involutions, these are Nikulin involutions which interchange two copies of E 8(-1) in the Néron Severi group.
Nikulin involutions on K3 surfaces / B. van Geemen, A. Sarti. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 255:4(2007 Apr), pp. 731-753.
Nikulin involutions on K3 surfaces
B. van GeemenPrimo
;
2007
Abstract
We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the 11-dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on Morrison-Nikulin involutions, these are Nikulin involutions which interchange two copies of E 8(-1) in the Néron Severi group.
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