MATH Seminar

Title: An arithmetic count of the lines on a cubic surface.
Seminar: Algebra
Speaker: Kirsten Wickelgren of Georgia Institute of Technology
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-11-14 at 4:00PM
Venue: W306
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Abstract: A celebrated 19th century result of Cayley and Salmon is that a smooth cubic surface over the complex numbers contains exactly 27 lines. Over the real numbers, it is a lovely observation of Finashin–Kharlamov and Okonek–Teleman that while the number of real lines depends on the surface, a certain signed count of lines is always 3. We extend this count to an arbitrary field k using an Euler number in A1-homotopy theory. The resulting count is valued in the Grothendieck-Witt group of non-degenerate symmetric bilinear forms. This is joint work with Jesse Kass.