dc.identifier.uri |
http://dx.doi.org/10.15488/216 |
|
dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/238 |
|
dc.contributor.author |
Hulek, Klaus
|
|
dc.contributor.author |
Spandaw, J.
|
|
dc.contributor.author |
van Geemen, B.
|
|
dc.contributor.author |
van Straten, D.
|
|
dc.date.accessioned |
2016-02-16T08:10:45Z |
|
dc.date.available |
2016-02-16T08:10:45Z |
|
dc.date.issued |
2001-08 |
|
dc.identifier.citation |
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 |
|
dc.description.abstract |
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. |
eng |
dc.language.iso |
eng |
|
dc.publisher |
Berlin : Walter de Gruyter |
|
dc.relation.ispartofseries |
Advances in Geometry 1 (2001), Nr. 3 |
|
dc.rights |
Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
|
dc.subject |
Calabi-Yau |
eng |
dc.subject |
algebra |
eng |
dc.subject |
applied mathematis |
eng |
dc.subject.classification |
Calabi-Yau-Mannigfaltigkeit |
ger |
dc.subject.classification |
Algebra |
ger |
dc.subject.classification |
Angewandte Mathematik |
ger |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
The modularity of the Barth-Nieto quintic and its relatives |
eng |
dc.type |
Article |
|
dc.type |
Text |
|
dc.relation.essn |
1615-7168 |
|
dc.relation.issn |
1615-715X |
|
dc.relation.doi |
http://dx.doi.org/10.1515/advg.2001.017 |
|
dc.bibliographicCitation.issue |
3 |
|
dc.bibliographicCitation.volume |
1 |
|
dc.bibliographicCitation.firstPage |
263 |
|
dc.bibliographicCitation.lastPage |
289 |
|
dc.description.version |
publishedVersion |
|
tib.accessRights |
frei zug�nglich |
|