Computational Algebra Seminar: Jahnel -- K3 surfaces with real multiplication

Our first seminar for the year will be given by Joerg Jahnel.

(Joerg is visiting the group until mid-March.)



K3 surfaces with real multiplication
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I will report on recent joint work with Andreas-Stephan Elsenhans (Sydney).

We construct explicit examples of K3 surfaces having real multiplication.

Our examples are of Picard rank 16. The standard method for computing the
Picard rank provably fails for the surfaces constructed. The existence of
K3 surfaces having real multiplication was proven before, using a
Hodge-theoretic approach, which did not lead to explicit equations. Our
approach involves a massive computer search using MAGMA.