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- Title
Order 3 symplectic automorphisms on K3 surfaces.
- Authors
Garbagnati, Alice; Prieto Montañez, Yulieth
- Abstract
The aim of this paper is to generalize results known for the symplectic involutions on K3 surfaces to the order 3 symplectic automorphisms on K3 surfaces. In particular, we will explicitly describe the action induced on the lattice Λ K 3 , isometric to the second cohomology group of a K3 surface, by a symplectic automorphism of order 3; we exhibit the maps π ∗ and π ∗ induced in cohomology by the rational quotient map π : X ⤏ Y , where X is a K3 surface admitting an order 3 symplectic automorphism σ and Y is the minimal resolution of the quotient X / ⟨ σ ⟩ ; we deduce the relation between the Néron–Severi group of X and the one of Y. Applying these results we describe explicit geometric examples and generalize the Shioda–Inose structures.
- Subjects
AUTOMORPHISMS; ISOMETRICS (Mathematics); MAPS
- Publication
Mathematische Zeitschrift, 2022, Vol 301, Issue 1, p225
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-021-02901-9