Algebraic Geometry Seminars

[Emilia Mezzetti]

UNIVERSITA' DI TRIESTE
DIPARTIMENTO DI MATEMATICA E GEOSCIENZE

ALGEBRAIC GEOMETRY SEMINARS

On Friday, March 16 2012, the following seminars will be held:

11:30
REMKE KLOOSTERMAN (HU Berlin)

THREEFOLDS WITH DEFECT AND NOETHER-LEFSCHETZ LOCI OF SURFACES


14:00
ADA BORALEVI (Università di Trieste & SISSA)

QUIVER REPRESENTATIONS, HOMOGENEOUS BUNDLES AND THE BGG RESOLUTION

Venue: Seminar room, Dipartimento di Matematica e Geoscienze,
Sezione di Matematica e Informatica (H2 building, Via Valerio 12/1).
All those interested are most welcome to attend.

ABSTRACTS

Threefolds with defect and Noether-Lefschetz loci of surfaces.

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.

Quiver representations, homogeneous bundles and the BGG resolution.

A quiver is a directed graph. Quivers come from combinatorics, and
homogeneous vector bundles from algebraic geometry. In 1990
Bondal and Kapranov established an equivalence of categories that
links together algebraic geometry, representation theory, and combinatorics.
To any homogeneous vector bundle on a rational homogeneous variety
they associate a finite dimensional 
representation of a given quiver (with relations).
In my talk I will describe this equivalence in detail. I will then explain a
conjectural link of the quiver representations with the
Bernstein-Gelfand-Gelfand category O, which could potentially
lead to an infinite dimensional version of the above mentioned equivalence.

-- 
Prof. Emilia Mezzetti

Dipartimento di Matematica e Informatica
Universita' di Trieste
Via Valerio 12/1
34127 Trieste, Italia

Stanza 227, II piano
e-mail: mezzette at units.it
tel. studio (+39) 040 558 2650
skype: emiliamezzetti
tel. Segreteria Dip.: (+39) 040 558 2635 oppure 2618
fax: (+39) 040 558 2636
http://www.dmi.units.it/~mezzette/