The University of Michigan Algebraic Geometry Seminar
Fall 2009: Wednesdays 4:10–6:00,  3088 East Hall

The seminar normally meets from 4:10 to about 6:00 pm, with a break around 5 pm. We encourage speakers to make the first hour of each talk expository and introductory in nature, so that this part of the seminar will be accessible to graduate students and postdocs in other fields. Details and technicalities are welcome (but not required!) after the break.

For more information, contact  Rob Lazarsfeld ( rlaz@umich.edu ) .

date speaker affiliation title (click for an abstract)
Sept. 16, 2009 Mark DeCataldo Stony Brook Topology of the Hitchin fibration and Hodge theory of character varieties
Sept. 23, 2009 Tommaso De Fernex Utah Rigidity properties of Fano varieties
Sept. 30, 2009 No seminar    
Oct. 7, 2009 Daniel Erman Berkeley Deformations of 0-dimensional schemes
Oct. 14, 2009 Yusuf Mustopa UMich Subordinate loci on symmetric products and syzygies of points
Oct. 21, 2009 Stephanie Yang KTH Stockholm Tautological rings of moduli spaces of curves
Oct. 28, 2009 No seminar   Ziwet lectures
Nov. 4, 2009
3:00–3:55:  4088 EH
5:15–6:15:  3088 EH
Kiran Kedlaya MIT and IAS Canonical determination of b-divisors, and formal classification of flat connections
Nov. 11, 2009 Jesse Kass UMich Extending families of Jacobians
Sat/Sun Nov 14–15 OSU/UIC/UM Weekend Algebraic Geometry Workshop
Nov. 18, 2009
3:00 : 4088 EH
Spencer Bloch Chicago More about the algebraic geometry of Feynman amplitudes
Nov. 18, 2009 Vikraman Balaji Chennai Analogue of the Narasimhan-Seshadri theorem in higher dimensions and holonomy
Nov. 25, 2009 No seminar Thanksgiving
Dec. 2, 2009 Dimitri Markushevich Lille, visiting UMich Tree-like compactification of the moduli space of rank 2 vector bundles over a projective surface
Dec. 9, 2009 Yu-jong Tzeng Stanford  

Thanks to Mike Zieve for the new web page!

Past Seminars: W09  F08  W08  F07 W07  F06  W06  F05 W05  F04  W04  F03 W03  F02  W02  F01 W01  F00  W00  F99  W99

Abstracts

Topology of the Hitchin fibration and Hodge theory of character varieties

Given a compact Riemann surface X of genus at least two, there are two algebraic varieties attached to it: the character variety Ch, and the Hitchin moduli space M. The non Abelian Hodge theorem asserts that they are diffeomorphic (but have different complex structures). While the rational cohomology rings H*(Ch) and H*(M) are isomorphic, the mixed Hodge structures are different and so are the weight filtrations, which therefore cannot possibly correspond via the non Abelian Hodge theorem.

In recent joint work with T. Hausel (Oxford) and L. Migliorini (Bologna) it is shown that the non Abelian Hodge theorem exchanges the weight filtration on H*(Ch) with the (perverse) Leray filtration on H*(M) for the Hitchin map h: MCn. Moreover, curious symmetries observed on H*(Ch) by number-theoretic means, turn out to be the more familiar Lefschetz and Poincaré symmetries for the map h. (The perverse Leray filtration is formally analogous to the Leray filtration associated with the Leray spectral sequence. However, as my on-line thesaurus states: "perverse = resistant to guidance or discipline.")


Rigidity properties of Fano varieties

I will discuss some deformation properties of Fano varieties. The general methods rely on the investigation of the variation of the cone of effective curves and, more generally, of the Mori chamber decomposition, which, according to Mori theory, encode information on the geometry of the variety. The talk is based on joint work with C. Hacon.


Deformations of zero-dimensional schemes

A natural question in the study of zero-dimensional schemes is to determine when such a scheme deforms to a disjoint union of points. I will discuss a syzygetic invariant which yields sharp information about this question. I will also give applications to the study of Hilbert schemes of points. This is joint work with M. Velasco.