Algebraic Geometry Seminar
Department of Mathematics
Princeton University
Fall 2003 Lectures
Regular meeting time:
Tuesdays 4:30--5:30
(Tea served at 3:30)
Place: Fine 322
| Date | Speaker | Title |
| Sep. 23 | F. Orgogozo Princeton |
Bloch's conductor formula and Milnor numbers
|
| Sep. 30 | Y.Tschinkel Uni. Goettingen |
On the arithmetic of K3 surfaces
|
| Oct.7 | O. Fujino Nagoya and IAS |
A canonical bundle formula.
|
| Oct.14 | R. Parimala Tata Inst |
Isotropy of quadratic forms over function fields
of p-adic curves.
|
| Oct.21 | Kiran S. Kedlaya IAS and MIT |
Semistable reduction for p-adic local systems.
|
| Oct.28 | Fall Break |
|
| Nov.4 | Alastair Craw Stony Brook |
Towards the McKay correspondence in all dimensions.
For a finite subgroup G of SL(3,C), Bridgeland, King and Reid
proved that a particular crepant resolution Y of the quotient C^3/G is
"distinguished" in the sense that it is a moduli space of objects on C^3.
In addition, they established the McKay correspondence for Y as an
equivalence of derived categories. I'll describe recent joint work with
Akira Ishii (Kyoto) proving that every crepant resolution of C^3/G is a
moduli space of representations of the McKay quiver (for G Abelian),
generalising a result by Kronheimer for finite subgroups of SL(2,C).
I'll also describe a programme to appropriately generalise the McKay
correspondence to higher dimensions.
|
| Nov.11 | |
|
| Nov.18 | Linda Chen Columbia |
The orbifold Chow ring of toric Deligne-Mumford stacks.
Orbifold cohomology and Chow ring theories have recently been
developed --
their invariants coincide with classical invariants of a nice (crepant)
resolution of singularities. We introduce a theory of toric
Deligne-Mumford stacks, compute their orbifold Chow rings, and give a
connection to resolutions of singularities. This is joint work with Lev
Borisov and Greg Smith.
|
| Nov.25 | Jaroslaw Wlodarczyk Purdue |
Simple Hironaka resolution.
Building upon works of O.Villamyor, Encinas-Villamayor and
Bierstone-Milman we give a short proof of Hironaka resolution teorems.
We put particular emphasis on canonicity and functoriality of
the algorithm. Introduced here idea of "Homogenized ideals" gives apriorie
canonicity of the resolution procedure and radically simplifies the proof.
|
| Dec.2 | Sorin Popescu Stony Brook |
Algebraic Sets of Minimal Degree.
Algebraic varieties of minimal degree were classified by
Del Pezzo (for surfaces) and Bertini (in all dimensions).
For various reasons the notion of ``minimal degree'' is not a
very sensible one for algebraic sets in general, but there are
other good geometric conditions that mean "minimal degree" in
the irreducible case and generalize well. In recent work with
Eisenbud, Green and Hulek we have achieved a rather
simple classification from which a number of surprising algebraic
and geometric results flow. It turns out also that this
classification coincides with that of 2-regular reduced ideals.
|
| Dec.9 | Gabriele Mondello |
Combinatorial and tautological classes on
the moduli space of curves.
Every presentation of the moduli space of curves gives rise to
"natural" cohomology classes. The so-called tautological classes appear in
the classical algebro-geometric setting. On the other side, the cellular
decomposition of the moduli space via the ribbon graph complex allowed
Witten to define some interesting cycles on it, which are called
combinatorial. The aim of this talk is to illustrate the main ideas
involved in the proof of the so-called Witten-Kontsevich
conjecture: combinatorial classes are tautological.
|
| Dec 11-14 | |
Katz Conference,
Information
|
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or this page, please email to:
kollar@math.princeton.edu.