Back to Algebraic Geometry Seminar: Spring 2016
Algebraic Geometry Seminar
Date: Tuesday, Feb 2, 2016
Time: 3:30PM - 4:30PM
Location: JFB 102
2:50 - 3:50PM JFB 102
Burt Totaro
University of California, Los Angelos
Title |
Hypersurfaces that are not stably rational |
Abstract |
We show that a large class of complex hypersurfaces in all dimensions are not stably rational. (A variety is stably rational if its product with some projective space is birational to projective space.) Namely, for all d at least about 2n/3, a very general hypersurface of degree d in P^{n+1} is not stably rational. The result covers all the degrees in which Kollar proved that a very general hypersurface is not rational, and a bit more. For example, very general quartic 4-folds are not stably rational, whereas it was not even known whether these varieties are rational. |
Algebraic Geometry