This analysis reveals properties of K3 surfaces with complex multiplication by CM fields, indicating possible transcendental and Picard lattices.
Let X be a complex projective K3 surface having complex multiplication by a CM field E , and let TX be its transcendental lattice. We say that X has maximal complex multiplication if EndHdg(TX) 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.
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Eva Bayer‐Fluckiger (2025) studied this question.
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