Yajnaseni Dutta : Counting lines on a cubic surface

Posted by Jeremy Kun , part of the Graduate Student Colloquium.

At

Oct. 12, 2015, 4 p.m.

In

BH 209

Abstract

A classical problem in algebraic geometry is to study the space of algebraic subspaces of an algebraic space. A cubic surface is a projective variety studied in algebraic geometry. It is an algebraic surface in three-dimensional projective space defined by a single algebraic equations of degree 3. One of the oldest and most beautiful statements in algebraic geometry is that on a smooth cubic surface there are exactly 27 lines. We begin with the classical approach, in a terms of cubic forms, and then proceed to the more modern approach, in which the cubic surface is considered as a blow up of the projective planes in 6 points. Food will be provided.