Algebraic Geometry Seminar
Spring 2009
Regular Day: Tuesday
Regular Time: 3:30PM - 4:30PM
Regular Location: LCB 215
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February 3 |
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February 10 |
Ana-Maria Castravet
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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.
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February 17 |
Marcello Bernardara
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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.
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March 2 3:00pm , LCB 215 |
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March 10 3:30pm, JWB 333 |
Paolo Stellari
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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.
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March 24 |
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March 31 |
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April 7 |
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April 28 |
Remi Lodh
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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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