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

Klaus Hulek, Remke Kloosterman (2011)

Annales de l’institut Fourier

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.

Comparaison des formes de Seifert et des fonctions zêta de Denef-Loeser des germes de courbe plane à singularité isolée

Philippe du Bois (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous démontrons que la donnée de la forme de Seifert entière et de la fonction zêta de Denef-Loeser d’un germe de courbe plane à singularité isolée ne déterminent pas le type topologique de ce germe. De plus, la fonction zêta de Denef-Loeser d’un tel germe ne détermine pas la forme de Seifert entière associée.

Complete intersection singularities of splice type as universal Abelian covers.

Neumann, Walter D., Wahl, Jonathan (2005)

Geometry & Topology

Complex surface singularities with integral homology sphere links.

Neumann, Walter D., Wahl, Jonathan (2005)

Geometry & Topology

Contact boundaries of hypersurface singularities and of complex polynomials

Clément Caubel, Mihai Tibăr (2003)

Banach Center Publications

We survey some recent results concerning the behavior of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.