UCSD Algebraic Geometry Seminar, Fall 2014

Meetings are held on Fridays, 2:30-3:30 pm, AP&M 7218.

October 17: Jorge Pereira (IMPA)
Title: Compact leaves of foliations
Abstract:I will discuss three questions on this talk.
(Existence) Given a smooth hypersurface Y of a projective manifold X with numerically trivial normal bundle, does there exist a codimension one foliation on X having Y as a compact leaf ?
(Abelian holonomy) What can we say about foliations having a compact leaf with abelian holonomy ?
(Factorization) It is rather easy to construct foliations on projective surfaces having compact leaves with non-solvable holonomy. In higher dimensions, the only known examples are pull-backs of foliations on surfaces through rational morphism. Is this a general phenomenon ? In particular, does the holonomy of compact leaves factor through curves when non solvable? (Joint work with B.Claudon, F. Loray, F. Touzet)
October 24: Charlie Siegel (IPMU)
Title: A Modular Operad of Embedded Curves
Abstract:Modular operads were introduced by Getzler and Kapranov to formalize the structure of gluing maps between moduli of stable marked curves. We present a construction of analogous gluing maps between moduli of pluri-log-canonically embedded marked curves, which fit together to give a modular operad of embedded curves. This is joint work with Satoshi Kondo and Jesse Wolfson.
October 31: Jie Wang (UCSD)
Title: Generic vanishing of Koszul cohomology: some recent progress
Abstract: A central problem in curve theory is to describe the extrinsic geometry of algebraic curves in a given projective space with fixed genus and degree. Koszul cohomology groups in some sense carry ’everything one ever wants to know’ about the defining equations of a curve X in r: the number of independent equations of each degree vanishing on X , the relations between the generators of the ideal IX of X, etc.

In this talk, I will describe an inductive approach to study Koszul cohomology groups of general curves. In particular, we show that to prove the Maximal Rank Conjecture (for quadrics), it suffices to check all cases with the Brill-Noether number ρ = 0. As a consequence, the Maximal Rank Conjecture holds if the embedding line bundles L on X satisfies the condition h1(L) < 3.

November 15: Special Day
Southern California Algebraic Geometry Day
The Fall Southern California Algebraic Geometry Day will be held at UCSD on Saturday, November 15 from 10am to 4pm in AP&M 6-402 (note the change from the seminar's usual time and location). The webpage for the seminar, including speakers and abstracts can be found here.

For titles and abstracts, please see also the mathematics department calendar.

Organizers: Elham Izadi, James McKernan and Dragos Oprea

This seminar is supported in part by grants from the NSF. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Past quarters: Fall 2013 , Winter 2014 , Spring 2014 .

The design of this webpage is copied shamelessly from the MIT Number Theory seminar site. Contact Cal Spicer at cwspicer@ucsd.edu about problems with the website or posters.