On a family of K3 surfaces with $\mathcal{S}_4$ symmetry

Details On a family of K3 surfaces with $\mathcal{S}_4$ symmetry On a family of K3 surfaces with $\mathcal{S}_4$ symmetry

2011-03-09

arxiv.org/abs/1103.1892v2

Mathematics

Algebraic Geometry

13 pages, 2 figures. Updated references. Comments are welcome!

Scientific paper

The largest group which occurs as the rotational symmetries of a three-dimensional reflexive polytope is the symmetric group on four elements. There are three pairs of three-dimensional reflexive polytopes with this symmetry group, up to isomorphism. We identify a natural one-parameter family of K3 surfaces corresponding to each of these pairs, show that the symmetric group on four elements acts symplectically on members of these families, and show that a general K3 surface in each family has Picard rank 19. The properties of two of these families have been analyzed in the literature using other methods. We compute the Picard-Fuchs equation for the third Picard rank 19 family by extending the Griffiths-Dwork technique for computing Picard-Fuchs equations to the case of semi-ample hypersurfaces in toric varieties. The holomorphic solutions to our Picard-Fuchs equation exhibit modularity properties known as "Mirror Moonshine"; we relate these properties to the geometric structure of our family.

Affiliated with

Also associated with

No associations

Rating

On a family of K3 surfaces with $\mathcal{S}_4$ symmetry 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 On a family of K3 surfaces with $\mathcal{S}_4$ symmetry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a family of K3 surfaces with $\mathcal{S}_4$ symmetry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-629668