K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups
Alice GarbagnatiUniversità degli Studi di Milano, Italy
Matteo PeneginiUniversità degli Studi di Milano, Italy
We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves by the diagonal action of either the group or the group where is an odd prime. These K3 surfaces admit a non-symplectic automorphism of order induced by an automorphism of one of the curves or . We prove that most of the K3 surfaces admitting a non-symplectic automorphism of order (and in fact a maximal irreducible component of the moduli space of K3 surfaces with a non-symplectic automorphism of order ) are obtained in this way.
In addition, we show that one can obtain the same set of K3 surfaces under more restrictive assumptions namely one of the two curves, say , is isomorphic to a rigid hyperelliptic curve with an automorphism of order and the automorphism of the K3 surface is induced by .
Finally, we describe the variation of the Hodge structures of the surfaces constructed and we give an equation for some of them.
Cite this article
Alice Garbagnati, Matteo Penegini, K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups. Rev. Mat. Iberoam. 31 (2015), no. 4, pp. 1277–1310DOI 10.4171/RMI/869