# Seminario: “Alexander polynomials of curves, Mordell-Weil ranks and syzygies”

## Mercoledì 19 Ottobre 2016, ore 14:30 - Sala Riunioni VII Piano - Remke Kloosterman

ARGOMENTI: Seminari

Mercoledì 19 Ottobre 2016 alle ore 14:30 in Sala Riunioni VII Piano, Remke Kloosterman terrà un seminario dal titolo “Alexander polynomials of curves, Mordell-Weil ranks and syzygies”.

Abstract
Fix a (singular) plane curve $C$. Recent results by Cogolludo-Agustin and Libgober, by Dimca suggest that there is an interesting interplay between
1. the Alexander polynomial of $C$. (A topological invariant)
2. the Mordell-Weil rank of certain isotrivial fibrations of abelian varieties with base $P^2$ and discriminant curve $C$. (An arithmetic invariant)
3. the Hilbert function of certain ideals of certain subschemes of the singular locus of $C$. (An algebraic invariant)
In this talk we will explain this interplay and refine it. Moreover, we will give various applications of this. In particular, if
$f(x,y,z)$ is a polynomial defining $C$ then we show how these results can be used to find all polynomials $(g,h)$ such that $g^2+h^3=f$.