# 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

**Abstract.**

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).