Algebraic geometry seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
January 31, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Xuntao Hu, Stony Brook University
Degeneration of abelian differentials and period matrices

The plumbing parameters give local coordinates near the boundary of the Deligne-Mumford compactification of the moduli spaces of Riemann surfaces. In this talk we introduce a new method to construct smooth abelian differentials on Riemann surfaces near an arbitrary degenerate Riemann surface, in terms of the plumbing parameters. This method further allows us to compute the degeneration of the period matrices, generalizing results of Yamada and Taniguchi.


Wednesday
February 07, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Greg Pearlstein, TAMU
Torelli theorems for special Horikawa surfaces and special cubic 4-folds

We will discuss recent work with Z. Zhang on Torelli theorems for bidouble covers of a smooth quintic curve and 2 lines in the plane, and cubic 4-folds arising from a cubic 3-fold and a hyperplane intersecting transversely in P^4.


Wednesday
February 14, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Michael Kemeny, Stanford
First steps toward a classification of Betti tables of canonical curves

Whilst Voisin's resolution of Green's conjecture gives a complete understanding of the shape of the Betti table of a canonical curve, we know very little about the values of the entries of the table. It is natural to hope that these entries contain new geometric information, and maybe even to dream of classifying possible tables in terms of geometry. We will talk about the very first step towards this, which is an analysis of one particular Betti number, namely the "extremal entry", i.e. the last entry on the first row. We will show that this entry records the number of minimal pencils possessed by the curve, counted with multiplicity. One actor in this story is Kleiman's inductive approach to the famous multiple point formula in intersection theory.


Wednesday
February 21, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Jian Xiao, Northwestern
Local positivity for curves

One of the most important invariants measuring the local positivity of a nef line bundle is the local Seshadri function introduced by Demailly. We first give a brief introduction to this invariant. Then using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants, studied also independently by M. Fulger, have nice properties similar to those for divisors. In particular, this enables us to obtain a Seshadri type ampleness criterion for movable curves, and give a characterization of the divisorial components of the non-ample locus of a big class. (Joint work with N. McCleerey.)


Wednesday
February 28, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Anna Cadoret, Jussieu/Courant
TBA

TBA


Wednesday
March 07, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Ariyan Javanpeykar, Mainz/Columbia
Arithmetic, algebraic, and analytic hyperbolicity

In the first part of this talk we will discuss different notions of hyperbolicity for algebraic varieties which are conjecturally related by conjectures of
Green-Griffiths, Lang, and Vojta. Then, we introduce an "analytic" notion of hyperbolicity, which interpolates between being Brody hyperbolic and
hyperbolically embedabble. I hope to give a survey of several known results in the first part. In the second part I will focus on arithmetic questions. For instance, Scholl proved that the
moduli of del Pezzo surfaces is arithmetically hyperbolic. In joint work with Daniel Loughran, we investigate the analogous question for Fano threefolds. For instance, we show that the
moduli of Fano threefolds is not arithmetically hyperbolic, by (explicitly) constructing an abelian surface which sits inside this moduli.


Wednesday
March 14, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Spring Break!, Stony Brook University
TBA

TBA


Wednesday
March 21, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Cristian Minoccheri, Stony Brook University
TBA

TBA


Wednesday
April 11, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Angela Gibney, Rutgers
TBA

TBA


Wednesday
April 18, 2018

4:00 PM - 5:30 PM
Math Tower P-131
David Hansen, Columbia
TBA

TBA


Wednesday
April 25, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Kenneth Ascher, MIT
TBA

TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars