Date/heure
27 mai 2019
15:30 - 16:30
Oratrice ou orateur
Zsolt Patakfalvi
Catégorie d'évènement Séminaire de géométrie complexe
Résumé
The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of polarized varieties, in particular on the base of families of Q-Fano varieties (that is, Fano varieties with klt singularities). It is conjectured that the CM line bundle yields a polarization on the conjectured moduli space of K-polystable Q-Fano varieties (which over the complex numbers are conjectured to be exactly the Fanos admitting a singular Kähler-Einstein metric). The above polarization conjecture boils down to showing semi-positivity and positivity statements about the CM-line bundle for families with K-semi-stable and K-polystable Q-Fano fibers, respectively. I present a joint work with Giulio Codogni where we prove the necessary semi-positivity statements in the K-semi-stable situation, and the necessary positivity statements in the uniform K-stable situation, including in both cases variants assuming K-stability only for very general fibers. Our statements work in the most general singular situation (klt singularities), and the proofs are algebraic, except the computation of the limit of a sequence of real numbers via the central limit theorem of probability theory.