Algebraic Geometry Seminar
Organizers：
Caucher Birkar，贾甲
Speaker：
Louis Esser
Princeton University
Time：
Fri., 9:00-10:00 am, Nov. 1, 2024
Online：
Zoom Meeting ID: 262 865 5007
Passcode: YMSC
Title：
Rational weighted projective hypersurfaces
Abstract：
Very general hypersurfaces in complex projective space (of dimension at least 3) are expected to be rational if and only if the degree is at most 2. T. Okada gave a similar "small degree condition" for weighted hypersurfaces that guarantees rationality and he proved that it is actually equivalent to rationality for a very general terminal quasismooth weighted hypersurface in dimension 3. In this talk, I'll show that there are rational examples in higher dimensions that don't satisfy this degree criterion. Along the way, I'll introduce two new rationality constructions for these hypersurfaces, which work over any field.
