University of Utah
Algebraic Geometry Seminar
Spring 2009: Tuesdays 3:30-4:30, LCB 215

Schedule of upcoming talks:

Click on the title of a talk for the abstract (if available).

Date Speaker Title
February 3 Emanuele Macrì
A categorical invariant for cubic threefolds
February 10
Ana-Maria Castravet
(University of Arizona)
Exceptional loci on moduli spaces of rational n-pointed curves The Grothendieck-Knudsen moduli space of stable, n-pointed rational curves is a fascinating variety whose geometry is still little understood. In particular, one would like to understand its effective cones (of curves or of divisors), its birational modifications, etc. A natural question is if boundary strata generate these cones. This is false for divisors by an example of Keel and Vermeire (for n=6) and still unknown for curves (this is known as the Fulton Conjecture). In some joint work with Jenia Tevelev, we identify the interior of the moduli space with a Brill-Noether locus of various very special reducible curves associated to hypergraphs. This allows us to construct factorially many new extremal (non-boundary) divisors of the effective cone, as well as some rigid curves and morphisms with small exceptional locus.
February 17
Marcello Bernardara
(Universität Bonn)
Stable pairs on elliptic K3 surfaces We consider a smooth K3 elliptic surface S with a section and we investigate the behaviour of moduli spaces of pairs on it. For a suitable choice of the framing, we get a finite family of moduli spaces related by wall crossing phenomena giving rise to birational maps. In a particular case, this allows to recover an isomorphism (described by Friedman with different techniques) between a moduli space of rank two coherent sheaves on S and the Hilbert scheme.
March 2
3:00pm, LCB 215
The seminar is canceled
March 10
3:30pm, JWB 333
Paolo Stellari
(Università di Milano)
Deformations of K3 surfaces and orientation We present a generalization of the Derived Torelli Theorem to first order deformations of the derived categories of K3 surfaces. This result shows that the equivalences between such categories is detected by the existence of special isometries of a first order deformation of the Mukai lattice. A key ingredient in the proof is the fact the such isometries preserve the orientation of a 4-dimensional subspace in the cohomology of the surfaces. This is joint work with E. Macrì and, partially, with D. Huybrechts.
March 24 Jimmy Dillies
On dessins d'enfants I
March 31 Aaron Bertram
Bridgeland stability and quasi-stability for surfaces, and some wild speculation in higher dimensions
April 7 Enka Lakuriqi
Introduction to Mirror Symmetry
April 28 Remi Lodh
On a generic hyperplane section of certain singular schemes over a field I will explain why a generic hyperplane section of a log-smooth scheme over a type of log-point is again log-smooth. A special case is that of toric singularities. We will make use of the language of logarithmic structures (in the sense of Fontaine-Illusie-Kato) and so we will give a brief introduction to this language.

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Program of Spring 2008

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This web page is maintained by Emanuele Macrì.