Abstract

Enumerative geometry is a branch of algebraic geometry that exploits the rigidity of algebraically-defined geometrical objects to prove unexpected combinatorial facts about them. One of the first nontrivial results of this type is the following (Cayley & Salmon 1849): There are exactly 27 distinct lines on any smooth cubic surface over C (i.e. nonsingular surface defined by the zeros of a cubic polynomial).

The talk will start with a discussion on the motivation and basic setting of classical algebraic geometry. We’ll then go through a partially elementary proof of Cayley & Salmon’s result, with a view towards the general methods for these kinds of problems.