| 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). |