10.15488/216
Hulek, Klaus
Spandaw, J.
van Geemen, B.
van Straten, D.
The modularity of the Barth-Nieto quintic and its relatives
Berlin : Walter de Gruyter
2001
Calabi-Yau
algebra
applied mathematis
Calabi-Yau-Mannigfaltigkeit
Algebra
Angewandte Mathematik
Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik
Technische Informationsbibliothek (TIB)
Technische Informationsbibliothek (TIB)
2016-02-16
2016-02-16
2001-08
eng
Article
Hulek, Klaus; Spandaw, J.; van Geemen, B.; van Straten, D.: The modularity of the Barth-Nieto quintic and its relatives. In: Advances in Geometry 1 (2001), Nr. 3, S. 263-289. DOI: http://dx.doi.org/10.1515/advg.2001.017
http://www.repo.uni-hannover.de/handle/123456789/238
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The moduli space of (1, 3)-polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y, respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L-function of their common third e A tale cohomology group is modular, as predicted by a conjecture of Fontaine and Mazur. The corresponding modular form is the unique normalized cusp form of weight 4 for the group Gamma(1)(6). By Tate's conjecture, this should imply that Y, the fibred square of the universal elliptic curve S-1(6), and Verrill's rigid Calabi-Yau ZA(3), which all have the same L-function, are in correspondence over Q. We show that this is indeed the case by giving explicit maps.