Algebraic Geometry Seminar
Eric Riedl
Notre Dame
Unirationality and strength of polynomials
Abstract: In a series of results dating back to Morin, it is shown that smooth hypersurfaces in a large number of variables are unirational. The basic technique shows an important relationship between the spaces of k-planes in these hypersurfaces and their unirationality. We investigate these questions using the notion of strength coming from commutative algebra. In particular, we prove that hypersurfaces having high secondary strength are also unirational, providing a new source of examples of (singular) unirational hypersurfaces. Along the way, we see that notions of strength allow for a very short proof of a weak form of the de Jong-Debarre conjecture. This is joint with Daniel Erman.
Monday November 3, 2025 at 3:00 PM in 636 SEO