2009/04/09 by Alice Garbagnati, Garbagnati, Alice
Mathematics · #14J10 #14J28 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.0904.1519
openalex publication_date 2009/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze K3 surfaces admitting an elliptic fibration E and a finite group G of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration E/G comparing its properties to the ones of E. We show that if E admits an n-torsion section, its quotient by the group of automorphisms induced by this section admits again an n-torsion section. Considering automorphisms coming from the base of the fibration, we can describe the Mordell--Weil lattice of a fibration described by Kloosterman. We give the isometries between lattices described by the author and Sarti and lattices described by Shioda and by Griees and Lam. Moreover we show that for certain groups H of G, H subgroups of G, a K3 surface which admits H as group of symplectic automorphisms actually admits G as group of symplectic automorphisms.