Speaker: Stephen McKean (Duke University)
Title: Rational lines on smooth cubic surfaces
Speaker's URL: https://services.math.duke.edu/~mckean/
Abstract: Over the complex numbers, every smooth cubic surface has 27 lines. A slightly less well-known fact (due to Schläfli) is that over the real numbers, every smooth cubic surface must have 3, 7, 15, or 27 lines. More generally, Segre proved that the number of lines on a smooth cubic surface over any field must be 0, 1, 2, 3, 5, 7, 9, 15, or 27. We will recall Segre’s geometric proof of this theorem and discuss which of these line counts are actually realized over various fields. Time permitting, we will also describe joint work with Minahan and Zhang on explicit formulas for the lines on a cubic surface in terms of three given skew lines.
URL associated with Seminar
https://research.math.osu.edu/agseminar/
