The elliptic modular surface of level 4 and its reduction modulo 3
Abstract
The elliptic modular surface of level 4 is a complex K3 surface with Picard number 20. This surface has a model over a number field such that its reduction modulo 3 yields a surface isomorphic to the Fermat quartic surface in characteristic 3, which is supersingular. The specialization induces an embedding of the N\'eron-Severi lattices. Using this embedding, we determine the automorphism group of this K3 surface over a discrete valuation ring of mixed characteristic whose residue field is of characteristic 3. The elliptic modular surface of level 4 has a fixed-point free involution that gives rise to the Enriques surface of type IV in Nikulin-Kondo-Martin's classification of Enriques surfaces with finite automorphism group. We investigate the specialization of this involution to characteristic 3.
Cite
@article{arxiv.1806.05787,
title = {The elliptic modular surface of level 4 and its reduction modulo 3},
author = {Ichiro Shimada},
journal= {arXiv preprint arXiv:1806.05787},
year = {2019}
}
Comments
32 pages. The proofs in Section 6 are simplified. The main results are not changed