On prime degree isogenies between K3 surfaces

TL;DR

This paper classifies prime order isogenies between algebraic K3 surfaces with non-isometric rational transcendental Hodge structures, revealing new types of correspondences beyond classical theorems.

Contribution

It provides a classification of prime degree isogenies between K3 surfaces that do not satisfy the Mukai--Nikulin theorem conditions, especially those arising from symplectic automorphisms.

Findings

Classified prime order isogenies with non-isometric Hodge structures

Identified algebraic correspondences beyond Mukai--Nikulin theorem

Described isogenies from K3 surfaces with symplectic automorphisms

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.