Algebraic Geometry Seminar
Spring 2011
Regular Day: Tuesday
Regular Time: 3:30PM - 4:30PM
Regular Location: LCB 323
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January 28 2-3pm, LCB 222 |
Chenyang Xu
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We show that the smooth locus of a log del Pezzo surface is not
only rationally connected but even strongly rationally
connected. This gives an affirmative answer to a conjecture due
to Hassestt-Tschinkel. It time permits, I will also talk about
applications of this result, namely to prove some classes of
del Pezzo surfaces over function fields of curves satisfy weak
approximations.
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February 1 |
Tyler Jarvis
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February 8 |
Daniel Erman
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The moduli space of n to 1 covers is well understood for n at
most 5, and it turns that these moduli spaces are best
understood in terms of a rather concrete question: when can the
ideal of n points in projective space be generated by the
minors of a matrix of linear forms? I will first explain some
of what was previously known about the moduli of degree n
covers, and then I will discuss some recent work on the case of
sextic covers. In particular, by illustrating a connection
with Gale duality, we identify local and global obstructions to
extending previous structural theorems to the sextic case. This
is joint work with Melanie Matchett Wood.
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| View details |
February 22 |
Alex Küronya
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The volume of a Cartier divisor on an irreducible projective
variety describes the asymptotic rate of growth of the number
of its global sections. As such, it is a non-negative real
number, which happens to be rational whenever the section ring
of the divisor in question is finitely generated.
In a joint work with Catriona Maclean and Victor Lozovanu we
study the multiplicative semigroup of volumes of divisors. We
prove that this set is countable on the one hand, on the other
hand it contains transcendental elements.
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| View details |
March 1 3-4pm, JWB 335 |
Tyler Jarvis
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The moduli of curves with W-structure and their corresponding
cohomological field theories form an orbifolded Landau-Ginzburg
A-model and are the subject of several beautiful mirror
symmetry conjectures. Some of these conjectures have been
proved, including the Witten ADE-integrable hierarchies
conjecture, while others are still open. In this talk I will
give an overview of the theory as well as discussing recent
progress on some of the conjectures, including the
Landau-Ginzburg/Calabi-Yau correspondence.
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| View details |
March 8 |
Mihai Fulger
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Given a normal variety X of dimension at least two, we fix a
point x on it and define a volume over x for any Cartier
divisor on an arbitrary birational model dominating X. This
volume function can be used to define and study a notion of
volume for a normal isolated singularity that is a
generalization of a volume introduced by J. Wahl for surface
singularities. We also compare our volume of isolated
singularities to a different recent generalization of Wahl's
work, as introduced by S.Boucksom, T. de Fernex and C. Favre.
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March 15 |
Dusty Ross
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The crepant resolution conjecture relates the GW theory of an
orbifold to the GW theory of a crepant resolution. We suspect
that the CRC for toric Calabi-Yau threefolds can be approached
locally via "open" GW theory. In this talk, I will lay out the
foundations for open GW theory of toric CY threefolds and
describe the recent success of the local approach for the
specific orbifold [O(-1)+O(-1)/Z_2] where the action is
trivial on the base and nontrivial on the fibers. This is
joint work with my advisor Renzo Cavalieri.
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| View details |
March 16 Wed, JWB 335 |
Martí Lahoz
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I will give a numerical criterion for the birationality of the
bicanonical map of a smooth irregular variety of arbitrary
dimension. The criterion is given in terms of the generic
vanishing of the canonical line bundle and related to the
properties of the Albanese map of the variety.
The study of the pluricanonical maps of varieties of maximal
Albense dimension was initiated by Chen and Hacon and has also
been developed by Pareschi and Popa. Part of the work I will
present has been done in collaboration with M.A. Barja,
J.C. Naranjo and G. Pareschi.
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March 29 |
Zach Teitler
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April 5 |
Stefan Kebekus
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April 12 |
Stefan Kebekus
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| View details |
April 15 1-2pm, LCB 222 |
Stefan Kebekus
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| View details |
April 26 |
Jeff Achter
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It has been known for some time that to a complex cubic surface
or threefold one can canonically associate a principally
polarized. I will explain a construction which works for
cubics over an arithmetic base, and discuss what this tells us
about the structure of the moduli space of cubic surfaces.
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