ODTÜ-BİLKENT
ALGEBRAIC GEOMETRY SEMINAR

“The Alexander module of a trigonal curve”

by

Alexander Degtyarev

Abstract:
The Alexander module of an
algebraic curve is a certain purely algebraic  invariant
of the fundamental group of (the complement of) the curve. Introduced by Zariski and developed by Libgober,
it is still a subject of intensive research. We will describe the Alexander
modules and Alexander polynomials (both over  Q and
over finite fields Fp ) of a special class
of curves, the so called generalized trigonal
curves.  The rational case is closed completely; in the case of
characteristic p>0, a few points remain open. (Conjecturally, all
polynomials that can appear are indeed listed.) Unlike most known divisibility
theorems, which rely upon the degree and the types of the singularities of the
curve, our bounds are universal: essentially, the Alexander module of a trigonal curve can take but a finitely many values.

Date:  1 October 2010 Friday

Time: 15:40

Place: Bilkent,
Mathematics Seminar Room SA-141

Tea and cookies will be served before the
talk.