**BİLKENT
ALGEBRAIC **

TOPOLOGY SEMINAR

**"Lines Generate the Picard Group of a Fermat
Surface"**

By

# ALEXANDER DEGTYAREV

# (Bilkent University)

** **

**Abstract:** We
answer a question of T. Shioda and show that, for any
positive integer m prime to 6, the Picard group of the Fermat surface _m
is generated by the classes of lines contained in _m.
More generally, for any integer m, the
classes of lines span a primitive subgroup of Pic_m.
These results admit an even further generalization (although not quite straightforward)
to Delsarte surfaces. In spite of the algebro-geometric setting, the proof is purely topologi- cal: it revolves about the topology of abelian coverings and the concept of Alexander module of a
plane curve.

**Date: ****Monday, October 7, 2013**

**Time: ****13.40-14.30**

**Place: ****Mathematics Seminar Room,
SA-141**

** **

**All are most cordially invited.**

Tea and cookies will be served after the talk.