|Title: An arithmetic count of the lines on a cubic surface.|
|Speaker: Kirsten Wickelgren of Georgia Institute of Technology|
|Contact: John Duncan, email@example.com|
|Date: 2017-11-14 at 4:00PM|
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 FinashinKharlamov and OkonekTeleman 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.
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