Computing the Lines of a Smooth Cubic Surface
Time: 2023-05-26
Published By: Wenqiong Li
Speaker(s): Hossein Movasati (IMPA and BIMSA)
Time: 14:00-15:00 May 30, 2023
Venue: Room 29, Quan Zhai, BICMR
We give an explicit formula for the 27 lines of a smooth cubic surface near the Fermat surface. Our formula involves convergent power series with coefficients in the extension of rational numbers with the sixth root of unity. Our main tool is the Artinian Gorenstein ring of socle two attached to such lines. If times permits, I will also describe how one can use similar tools to construct a conjectural counterexample to a conjecture of Harris on special components of Noether-Lefschetz loci for degree eight surfaces.
