MERCOLEDI' 21 MARZO 2012
15:00-16:00, Sala Riunioni (Dip. Matematica)
SEMINARI DI GEOMETRIA
Threefolds with defect and Noether-Lefschetz loci of surfaces Remke Kloosterman (Humboldt Universitaet, Berlino)
On a smooth variety every Weil divisor is a Cartier divisor. An obvious question
is then how singular a variety needs to be in order to have a Weil divisor that
is not a Cartier divisor.
In the case of nodal hypersurfaces in P
^4
Cheltsov determined the
minimal number of singular points to have such a
Weil divisor.
We present a different approach to prove Cheltsov's result
using the explicit Noether-Lefschetz theorem of Green and Voisin and the theory
of syzygies. We show how this new approach can be generalized to classes of
hypersurfaces and complete intersections where Cheltsov's approach does not seem
to work.