30.11.21

Florent Schaffhauser (Universidad de los Andes and Université de Strasbourg)

Title

Hodge and Betti numbers of real algebraic varieties, a walk
through a few examples

Abstract

By the famous Smith-Thom inequality, the total mod 2 Betti
number of the real locus of a real algebraic variety is constrained by the total mod 2 Betti number of its complex locus. When the variety is smooth and projective, it also carries Hodge numbers, from which the rational Betti numbers of the variety can be recovered. It turns out that, in a lot of significant examples, the Betti numbers of the real locus are constrained by the Hodge numbers of the complex locus. We shall present this property through a personal selection of such examples and explain how it can be used to prove that certain moduli spaces defined over the reals provide new, interesting families of so-called maximal real varieties.

Schedule

10:00 - 11:30 RTG Lecture 1 | on zoom

11:30 - 12:00 Get-Together with speaker | on zoom

13:00 - 13:30 Informal meeting of PhD students | on zoom

13:30 - 14:30 RTG colloquium: Florent Schaffhauser | on zoom

15:00 - 16:30 RTG Lecture 2 | In Karlsruhe, Room SR1.067, and on zoom

HD