Algebraic Geometry Seminar Fall 2013

The seminar meets on Fridays at 2:25 pm in Van Vleck B219.

The schedule for the previous semester is here.

Spring 2013

date	speaker	title	host(s)
September 6	Matt Baker (Georgia Institute of Technology)	Metrized Complexes of Curves, Limit Linear Series, and Harmonic Morphisms	Melanie, Jordan
September 13	Nick Addington (Duke)	Hodge theory and derived categories of cubic fourfolds	Andrei

Abstracts

Matt Baker

Metrized Complexes of Curves, Limit Linear Series, and Harmonic Morphisms

A metrized complex of algebraic curves is a finite edge-weighted graph G together with a collection of marked complete nonsingular algebraic curves C_v, one for each vertex; the marked points on C_v correspond to edges of G incident to v. We will present a Riemann-Roch theorem for metrized complexes of curves which generalizes both the classical and tropical Riemann-Roch theorems, together with a semicontinuity theorem for the behavior of the rank function under specialization of divisors from smooth curves to metrized complexes. As an application of the above considerations, we formulate a generalization of the notion of limit linear series to semistable curves which are not necessarily of compact type. This is joint work with Omid Amini. If time permits, we will also discuss how harmonic morphisms of metrized complexes can be used to provide a generalization of the Harris-Mumford theory of admissible coverings (joint work with Amini, Brugalle, and Rabinoff). This provides a "tropical" description of the tame fundamental group of an algebraic curve.