Algebraic Geometry Seminar
Spring 2011 — Tuesdays 3:304:30, LCB 323
Date  Speaker  Title — click for abstract (if available) 
January 28 23pm, LCB 222 
Chenyang Xu MIT 
Strong rational connectedness of open surfaces
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 HassesttTschinkel. 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.

February 1 
Tyler Jarvis BYU 
Rescheduled: March 1 
February 8 
Daniel Erman Stanford 
Sextic covers and Gale duality
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.

February 22 
Alex Küronya Freiburg 
Arithmetic properties of volumes of divisors
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 nonnegative 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. 
March 1 34pm, JWB 335 
Tyler Jarvis BYU 
Moduli of Curves with Wstructure, Mirror Symmetry, and the
LandauGinzburg/CalabiYau correspondence
The moduli of curves with Wstructure and their corresponding
cohomological field theories form an orbifolded LandauGinzburg
Amodel and are the subject of several beautiful mirror
symmetry conjectures. Some of these conjectures have been
proved, including the Witten ADEintegrable 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
LandauGinzburg/CalabiYau correspondence.

March 8 
Mihai Fulger Univ. of Michigan 
Local volumes
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.

March 15 
Dusty Ross Colorado State 
Open GromovWitten Theory and the Crepant Resolution Conjecture
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 CalabiYau 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.

March 16 Wed, JWB 335 
Martí Lahoz Univ. de Barcelona 
Bicanonical map of higher dimensional irregular varieties
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. 
March 29 
Zach Teitler Boise State 
TBA 
April 5 
Stefan Kebekus Freiburg 
Extension properties of differentials and applications I 
April 12 
Stefan Kebekus Freiburg 
Extension properties of differentials and applications II 
April 15 12pm, LCB 222 
Stefan Kebekus Freiburg 
Extension properties of differentials and applications III 
April 26 
Jeff Achter Colorado State 
Arithmetic Torelli maps for cubic surfaces and threefolds
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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