Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces

Klaus Hulek[1]; Remke Kloosterman[2]

  • [1] Leibniz Universität Hannover Institut für Algebraische Geometrie Welfengarten 1 30167 Hannover (Germany)
  • [2] Humboldt Universität zu Berlin Institut für Mathematik Unter den Linden 6 10099 Berlin (Germany)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 3, page 1133-1179
  • ISSN: 0373-0956

Abstract

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In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective 4 -space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.

How to cite

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Hulek, Klaus, and Kloosterman, Remke. "Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces." Annales de l’institut Fourier 61.3 (2011): 1133-1179. <http://eudml.org/doc/219798>.

@article{Hulek2011,
abstract = {In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective $4$-space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.},
affiliation = {Leibniz Universität Hannover Institut für Algebraische Geometrie Welfengarten 1 30167 Hannover (Germany); Humboldt Universität zu Berlin Institut für Mathematik Unter den Linden 6 10099 Berlin (Germany)},
author = {Hulek, Klaus, Kloosterman, Remke},
journal = {Annales de l’institut Fourier},
keywords = {Mordel-Weil group of Elliptic threefolds; Cohomology of singular varieties; Mixed Hodge structures; Mordell-Weil group of elliptic threefolds; cohomology of singular varieties; mixed Hodge stuctures},
language = {eng},
number = {3},
pages = {1133-1179},
publisher = {Association des Annales de l’institut Fourier},
title = {Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces},
url = {http://eudml.org/doc/219798},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Hulek, Klaus
AU - Kloosterman, Remke
TI - Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 3
SP - 1133
EP - 1179
AB - In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective $4$-space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.
LA - eng
KW - Mordel-Weil group of Elliptic threefolds; Cohomology of singular varieties; Mixed Hodge structures; Mordell-Weil group of elliptic threefolds; cohomology of singular varieties; mixed Hodge stuctures
UR - http://eudml.org/doc/219798
ER -

References

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