The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces

Details The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces

2008-12-24

arxiv.org/abs/0812.4518v2

Mathematics

Algebraic Geometry

11 pages. Arguments revised, results unchanged. Final version, to appear in Proc. Amer. Math. Soc

Scientific paper

We prove that if a K3 surface $X$ admits $\Z/5\Z$ as group of symplectic automorphisms, then it actually admits $\Dh_5$ as group of symplectic automorphisms. The orthogonal complement to the $\Dh_5$-invariants in the second cohomology group of $X$ is a rank 16 lattice, $L$. It is known that $L$ does not depend on $X$: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. We also give an elementary construction of $L$.

Affiliated with

Also associated with

No associations

Rating

The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces 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 The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-395964