On prime degree isogenies between K3 surfaces
Algebraic Geometry
2022-03-15 v1
Abstract
We classify prime order isogenies between algebraic K3 surfaces whose rational transcendental Hodges structures are not isometric. The morphisms of Hodge structures induced by these isogenies are correspondences by algebraic classes on the product fourfolds; however, they do not satisfy the hypothesis of the well-known Mukai--Nikulin theorem. As an application we describe isogenies obtained from K3 surfaces with an action of a symplectic automorphism of prime order.
Cite
@article{arxiv.1510.07465,
title = {On prime degree isogenies between K3 surfaces},
author = {Samuel Boissière and Alessandra Sarti and Davide Cesare Veniani},
journal= {arXiv preprint arXiv:1510.07465},
year = {2022}
}