Algebraic Geometry Seminar
Department of Mathematics
Princeton University
Fall 2008 Lectures
Regular meeting time:
Tuesdays 4:30-5:30 (Tea served at 3:30)
Place: Fine 322
| Date | Speaker | Title |
| Sep 16 | Benedict Gross Harvard University |
On the restriction of irreducible representations of the
group Un(k) to the subgroup Un-1(k)
Abstract |
| Sep 23 | Ulrich Derenthal Universität Zürich/Princeton University |
Rational points on cubic surfaces
Cubic surfaces defined over the field of rational numbers often contain infinitely many rational points. A conjecture of Manin predicts the distribution of these points precisely. This talk will give an introduction to the universal torsor approach to this conjecture and report on current progress in the case of singular cubic surfaces. |
| Sep 30 | Gueorgui Todorov Princeton University |
Pluricanonical maps on threefolds
We will discuss the problem of effectiveness of Iitaka fibrations for surfaces and threefolds. |
| Oct 7 | Yuri Tschinkel New York University |
A Torelli theorem over finite fields
I will discuss a set-theoretic analog of the classical Torelli theorem for curves. |
| Oct 14 | Florin Ambro Romanian Academy of Sciences/ Johns Hopkins |
On the cone theorem
I will discuss the structure of the ample cone for varieties with log canonical singularities, or certain reducible varieties. |
| Oct 21 | Frans Oort University of Utrecht/ Columbia university |
Leaves in moduli spaces in characteristic p
We try to understand the geometry of the moduli space of polarized abelian varieties in characteristic p. E.g. the phenomenon that Hecke orbits blow up and down in a rather unpredictable way. Choose a point x, corresponding to a polarized abelian variety. We study C(x) consisting of all moduli points of polarized abelian varieties which have the same p-adic and \ell-adic invariants. This turns out to be a locally closed subset. We discuss properties of these sets, which form a foliation of the related Newton polygon stratum. We give several applications. |
| Oct 28 | Fall break |
No seminar
|
| Nov 4 | Harry Tamvakis University of Maryland |
|
| Nov 11 | Osamu Fujino Nagoya University |
|
| Nov 18 | Sabin Cautis Rice University |
|
| Nov 25 | Brian Conrad Stanford University |
Finiteness theorems for algebraic groups over function
fields
If X is a smooth variety over a global field k, G is an algebraic group over k equipped with an action on X, and x is a point in X(k) then it is natural to ask how the property of x' in X(k) being in the G(k)-orbit of x compares with being in the G(k_v)-orbit of x for all places v of k. In general there is a non-trivial "local-to-global" obstruction space, but one can ask if it is finite. Even when G is semisimple, this finiteness problem leads to the consideration of the isotropy group G_x that is generally not connected or reductive (or even smooth when char(k) > 0). In the number field case the finiteness of these obstruction spaces was proved by Borel and Serre long ago, but their method used characteristic 0 in an essential way. Recently in joint work with Gabber and G. Prasad we have developed a theory of "pseudo-reductive groups" which is a very useful tool to prove results for general affine algebraic groups in the function field case that were previously known only in the reductive case. In particular, this work makes it possible to prove the analogue of the Borel-Serre finiteness result over function fields (away from char. 2 for now). The first part of the talk will explain a bit about the theory of pseudo-reductive groups, and the rest of the talk will show how it is used to establish the finiteness of the local-to-global obstruction spaces in the function field case (in char. > 2). If time permits we will also discuss an application to the problem of whether the k-isomorphism class of a projective k-variety is determined (up to "finite ambiguity") by its k_v-isomorphism class for all places v of k (a problem solved by Mazur over number fields, once again making essential use of characteristic 0). |
| Dec 2 | Eduardo Esteves Instituto de Matematica Pura e Aplicada |
|
| Dec 9 | David Smyth Harvard University |
|
Previous semester schedule (spring
2008)
Other seminars in this department
For more information about this seminar, contact Samuel Grushevsky (sam@math) and Max Lieblich (lieblich@math).