Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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On osculating cones to Brill-Noether loci

Michael Hoff

created by risa on 20 Nov 2015

26 nov 2015 -- 15:15

Aula 211, Dip. Matematica, Università "Roma Tre", Roma


Let C be a general canonical embedded curve of genus g and let $W_d(C)$ be the Brill-Noether locus. In an article from 1988, Kempf and Schreyer studied the geometry of the osculating cone to the theta divisor $W_{g-1}(C)$ at a general singular point and showed that one can recover the curve C from the osculating cone. We believe that similar results are true for all $W_d(C)$. In my talk, I will describe the osculating cone to $W_d(C)$ at a smooth isolated point of $W^1_d(C)$ (hence an isolated singularity of $W_d(C)$) for C of even genus g=2(d-1). In particular, I will show that the curve C is a component of the osculating cone. The proof is based on techniques introduced by Kempf in 1986. This is joint work with Ulrike Mayer (Saarland University).

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