## How to count lines on a cubic surface arithmetically

### Jesse Kass – University of South Carolina

Salmon and Cayley proved the celebrated 19th century result that a smooth cubic surface over the complex numbers contains exactly 27 lines. By contrast, the count over the real numbers depends on the surface, and these possible counts were classified by Segre. Benedetti–Silhol, Finashin–Kharlamov and Okonek––Teleman made the striking observation that Segre’s work shows a certain signed count is always 3. In my talk, I will explain how to extend this result to an arbitrary field. Although I will not use any homotopy, I will draw motivation from A1-homotopy theory. This is joint work with Kirsten Wickelgren.