**Department of Mathematics**

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

**Classification of simple quartics up to equisingular
deformation-I**

**ÇİSEM GÜNEŞ**

**(BİLKENT UNIVERSITY)**

Abstract: In this talk we discuss the problem of classifying
complex non-special simple quartics up to equisingular deformation by reducing the problem to an
arithmetical problem about lattices. On this arithmetical side, after applying Nikulin's existence theorem, our computation based on the
Miranda-Morrison's theory computing the genus groups. We give a complete
description of equisingular strata of non-special
simple quartics.

First we recall fundamentals of Nikulin's theory of discriminant forms and lattice
extensions and give a brief introduction to Miranda-Morrison's theory and
recast some of their results in a form more suitable for our computations. Then
we recall the notion of abstract homological types and arithmetical reduction
of classification problem. Finally we give ideas of the proof of our principal
result.

** **

** **

**Date: ****Friday, November 18, 2016**

**Time: ****15.40-**

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

You are most cordially invited Tea and cookies
will be served before the seminar.