Alice Garbagnati, Yulieth Prieto Montañez
Published 2022-09-21Version 1
A Shioda--Inose structure is a geometric construction which associates to an Abelian surface a projective K3 surface in such a way that their transcendental lattices are isometric. This geometric construction was described by Morrison by considering special symplectic involutions on the K3 surfaces. After Morrison several authors provided explicit examples. The aim of this paper is to generalize Morrison's results and some of the known examples to an analogous geometric construction involving not involutions, but order 3 automorphisms. Therefore we define the generalized Shioda--Inose structures of order 3, we identify the K3 surfaces and the Abelian surfaces which appear in these structures and we provide explicit examples.
Comments: 32 pages. In the published version of arXiv:2102.01207v1 the last section was erased. This paper contains an extended version of that section, with the details of the proofs, together with many examples, remarks and explicit constructions which are new
On K3 surface quotients of K3 or Abelian surfaces
An abelian surface with (1,6)-polarisation
Free automorphism groups of K3 surfaces with Picard number 3
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