SMS scnews item created by John Enyang at Sun 17 Feb 2013 1350
Type: Seminar
Modified: Fri 22 Feb 2013 1308; Fri 22 Feb 2013 1311
Distribution: World
Expiry: 2 Mar 2013
Calendar1: 1 Mar 2013 1205-1255
CalLoc1: Carslaw 454
Auth: enyang@penyang.pc (assumed)

Algebra Seminar

Stability for (bi)canonical curves


Friday 1st March, 12:05-12:55pm, Carslaw 454 - Please note the revised location


Jarond Alper (Australian National University)


Stability for (bi)canonical curves


The classical construction of the moduli space of curves, \( M_g \), via Geometric Invariant Theory (GIT) relies on the asymptotic stability result of Gieseker that the m-th Hilbert Point of a pluricanonically embedded smooth curve is GIT-stable for all sufficiently large \( m \). Several years ago, Hassett and Keel observed that if one could carry out the GIT construction with non-asymptotic linearizations, the resulting models could be used to run a log minimal model program for the space of stable curves. A fundamental obstacle to carrying out this program is the absence of a non-asymptotic analogue of Gieseker's stability result, i.e. how can one prove stability of the \(m\)-th Hilbert point for small values of \(m\)?

In this talk, we'll begin with a basic discussion of geometric invariant theory as well as how it applies to construct \(M_g\) in order to introduce and motivate the essential stability question in which this procedure rests on. The main result of the talk is: the \( m \)-th Hilbert point of a general smooth canonically or bicanonically embedded curve of any genus is GIT-semistable for all \(m > 1\). This is joint work with Maksym Fedorchuk and David Smyth.


We will take the speaker to lunch after the talk.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang

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