**ODTÜ-B****Ý****LKENT
ALGEBRAIC GEOMETRY SEM****I****NAR**

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**“****Exceptional
Belyi Coverings****”**

By

**ALEXANDER KLYACHKO**

**(**Bilkent University**)**

**Abstract: **(This is a joint project with Cemile Kürkoðlu.) Exceptional
covering is a connected Belyi covering uniquely
determined by its ramification scheme. Well known examples are cyclic,
dihedral, and Chebyshev coverings. We add to this
list a new infinite series of rational exceptional coverings together with the
respective Belyi functions. We shortly discuss the minimal field of
definition of a rational exceptional covering and show that it is either Q or
its quadratic extension. Existing theories give no upper bound on degree of the
field of definition of an exceptional covering of genus 1. It is an open
question whether the number of such coverings is finite or infinite. Maple search for an exceptional covering of
g>1 found none of degree 18 or less. Absence
of exceptional hyperbolic coverings is a mystery we couldn’t explain.

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** **

**Date: ****Friday, April 24, 2015**

**Time: ****15.40**

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

Tea and cookies will be served before the
seminar.