English

Real and complex multiplication on K3 surfaces via period integration

Algebraic Geometry 2022-04-12 v3 Algebraic Topology Number Theory

Abstract

We report on a new approach, as well as some related experiments, to construct families of K3 surfaces having real or complex multiplication. The approach is based on an explicit description of the transcendental part of the cohomology in a topological way, using topological tori. Fundamental ideas include considering the period space of marked K3 surfaces, determining the periods by numerical integration, as well as tracing the modular curve by a numerical continuation method.

Keywords

Cite

@article{arxiv.1802.10210,
  title  = {Real and complex multiplication on K3 surfaces via period integration},
  author = {Andreas-Stephan Elsenhans and Jörg Jahnel},
  journal= {arXiv preprint arXiv:1802.10210},
  year   = {2022}
}

Comments

Minor revision

R2 v1 2026-06-23T00:36:04.232Z