We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves C 1 ×C 2 by the diagonal action of either the group \Z/p\Z or the group \Z/2p\Z. These K3 surfaces admit a non-symplectic automorphism of order p induced by an automorphism of one of the curves C_1 or C_2 . We prove that most of the K3 surfaces admitting a non-symplectic automorphism of order p (and in fact a maximal irreducible component of the moduli space of K3 surfaces with a non-symplectic automorphism of order p ) are obtained in this way.Inaddition, we show that one can obtain the same set of K3 surfaces under more restrictive assumptions namely one of the two curves, say C_2 , is isomorphic to a rigid hyperelliptic curve with an automorphism \delta_p of order p and the automorphism of the K3 surface is induced by \delta_p. Finally, we describe the variation of the Hodge structures of the surfaces constructed and we give an equation for some of them.
K3 surfaces with a non-symplectic automorphism and product-quotient surfaces / A. Garbagnati, M. Penegini. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 31:4(2015), pp. 1277-1310.
|Titolo:||K3 surfaces with a non-symplectic automorphism and product-quotient surfaces|
|Parole Chiave:||K3 surfaces; automorphisms of K3 surfaces; product-quotient surfaces|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Progetto:||Geometria delle Varietà Algebriche|
|Data di pubblicazione:||2015|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4171/RMI/869|
|Appare nelle tipologie:||01 - Articolo su periodico|