Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms

Details Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms

2009-04-09

arxiv.org/abs/0904.1519v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-408689