How to count lines on a cubic surface arithmetically

Series: Algebraic Geometry Seminar
Location: ENR 2 S395
Presenter: Jesse Kass, University of South Carolina

A celebrated 19th century result is that a smooth cubic surface over the complex numbers contains exactly 27 lines.  Over the real numbers, the count of lines depends on the surface, but Segre showed that a certain signed count is independent of the surface.  In my talk, I will explain how to extend Segre’s to an arbitrary field.  This result is an application of recent ideas about Euler classes in A1-homotopy theory.  All work is joint with Kirsten Wickelgren.