Generalised Kummer constructions and Weil restrictions

2007/10/24 by Slawomir Cynk, Cynk, Slawomir, Matthias Schuett +1 · 1 citation
Mathematics · #11G40 #14G10 #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G40 #msc:14G10 #msc:14J32

paper · pdf · doi:10.48550/arxiv.0710.4565

12 pages; v2: added references, minor changes

arxiv created 2008/08/25 · arxiv updated 2009/12/01

Abstract

We use a generalised Kummer construction to realise all but one known weight four newforms with complex multiplication and rational Fourier coefficients in smooth Calabi-Yau threefolds defined over the rational numbers. The Calabi-Yau manifolds are smooth models of quotients of the Weil restrictions of elliptic curves with CM of class number three.

Cited by

• Finite groups of matrices over quadratic number fields

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• Calabi-Yau Manifolds Over Finite Fields, I
• A rigid Calabi--Yau 3-fold
• Rational curves on Calabi-Yau threefolds and a conjecture of Oguiso