Conférence GAGC 2016 (en 2017)

On the unirationality of Hurwitz spaces

Non programmé

50m

CIRM, Luminy

Orateur

Fabio Tanturri

Description

In this talk I will discuss about the unirationality of the Hurwitz spaces $H_{g,d}$ parametrizing d-sheeted branched simple covers of the projective line by smooth curves of genus $g$. I will summarize what is already known and formulate some questions and speculations on the general behaviour. I will then present a proof of the unirationality of $H_{12,8}$ and $H_{13,7}$, obtained via liaison and matrix factorizations. This is part of two joint works with Frank-Olaf Schreyer. Les résultats dont je voudrais parler sont contenus dans les travaux "Matrix factorizations and curves in ${\mathbb{P}}^4$" (https://arxiv.org/abs/1611.03669) et "Unirational Hurwitz spaces and liaison" (en préparation).