Séminaires : Séminaire de géométrie algébrique

Equipe(s) : tga,
Responsables :
Email des responsables :
Salle : http://www.imj-prg.fr/tga/sem-ga
 Orateur(s) Chen Jiang - , Titre Positivity in hyperkähler manifolds via Rozansky-Witten theory Date 21/01/2021 Horaire 14:00 à 15:00 Diffusion Résume L'exposé sera diffusé (396 751 8661, demander le mot de passe à Oliver B. ou D. ou Frederic H.) Abstract: For a hyperk\"{a}hler manifold $X$ of dimension $2n$, Huybrechts showed that there are constants $a_0, a_2, \dots, a_{2n}$ such that $$\chi(L) =\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q_X(c_1(L))^{i}$$ for any line bundle $L$ on $X$, where $q_X$ is the Beauville--Bogomolov--Fujiki quadratic form of $X$. Here the polynomial $\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q^{i}$ is called the Riemann--Roch polynomial of $X$. In this talk, I will discuss recent progress on the positivity of coefficients of the Riemann--Roch polynomial and also positivity of Todd classes. Such positivity results follows from a Lefschetz-type decomposition of the root of Todd genus via the Rozansky—Witten theory, following the ideas of Hitchin, Sawon, and Nieper-Wißkirchen. Salle http://www.imj-prg.fr/tga/sem-ga Adresse