University of Cambridge > > The Archimedeans > 27 lines on a smooth cubic

27 lines on a smooth cubic

Add to your list(s) Download to your calendar using vCal

  • UserDavid Bai
  • ClockFriday 08 April 2022, 15:00-16:00
  • HouseZoom.

If you have a question about this talk, please contact zl474.

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.

This talk is part of the The Archimedeans series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity