dr. Tanturri's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT


Wed, 12 June, at 16:30

Fabio Tanturri (SISSA)

Hilbert schemes of degeneracy loci

Abstract:
Given a morphism F between vector bundles on P^N=P(V), its (first)
degeneracy locus X is made up of points in which the morphism has not
maximal rank; locally, X is cut by the maximal minors of the matrix
representing F.
Interesting questions arise when one wants to give a parametrization of such
degeneracy loci, by looking at the union of the irreducible components 
of the
Hilbert Scheme H_X containing the general X's. I will focus on the case in
which the morphism is given by m global sections of Omega(2), the twisted
cotangent sheaf on P(V). In this case, making use of the Kempf-Weyman's
method for computing syzygies via resolutions of singularities, H_X can be
proved to be birational to the Grassmannian Gr(m, Lambda^2 (V)), when
3 < m < N. If m=3, the Grassmannian is birational to a subscheme of H_X,
a nice geometric description of which can be given.

VENUE: Room 136