Year: 2025
Type: article
Abstract: Let X be a complex projective K3 surface having complex multiplication by a CM field E , and let T_{X} be its transcendental lattice. We say that X has maximal complex multiplication if \mathrm{End}_{\mathrm{Hdg}}(T_{X}) is the ring of integers of E .For which CM fields E does such a K3 surface exist? What are the possibilities for the transcendental lattices, Picard lattices of these surfaces? The aim of this paper is to study these questions and give some examples.
Source: Documenta Mathematica
DOI: 10.4171/dm/1030
Author: Eva Bayer-Fluckiger
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413833180