# Journées de Géométrie Algébrique Poitiers-Bordeaux

24-25 November 2016
Poitiers
Europe/Paris timezone

## Nodal hypersurfaces with defect, Alexander polynomials and Mordell-Weil groups

24 Nov 2016, 10:40
50m
0-6 (Poitiers)

Board: 2
Exposé de 50 min

### Speaker

Prof. Remke Kloosterman

### Description

In this talk we present a short proof for Cheltsov's result that a nodal hypersurface of degree $d$ in $P^4$ which is not factorial, has at least $(d-1)^2$ nodes. We will discuss how variants of these arguments yields interesting results on the fundamental group of the complement of a singular plane curve and on the Mordell-Weil group of certain abelian varieties over function fields of characteristic zero.

### Presentation Materials

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