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.