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On the motive of Kummer varieties associated to $\Gamma_1(7)$ - Supplement to the paper: The modularity of certain non-rigid Calabi-Yau threefolds (by R. Livn\'e and N. Yui) by Hulek, Klaus; Verrill, Helena is a scholarly article available to read on EtoBox.

What is On the motive of Kummer varieties associated to $\Gamma_1(7)$ - Supplement to the paper: The modularity of certain non-rigid Calabi-Yau threefolds (by R. Livn\'e and N. Yui) about?

In their paper Livn\'e and Yui (math.AG/0304497) discuss several examples of non-rigid Calabi-Yau varieties which admit semi-stable K3-fibrations with 6 singular fibres over a base which is a rational modular curve. They also establish the modularity of the L-function of these examples. The purpose of this note is to point out that the examples which were listed in their paper, but which do not lead to semi-stable fibrations, are still modular in the sense that their L-function is associated to modular forms. We treat the case associated to the group Gamma_1(7) in detail, but our technique also applies to many other cases. We further make some comments concerning the Kummer construction for fibre products of elliptic surfaces in general.

Author

Hulek, Klaus; Verrill, Helena

Published

2005

Language

EN