Научный семинар Лаборатории алгебраической геометрии и ее приложений: Сесиль Гаше, Ницца (онлайн семинар)

На семинаре выступит Сесиль Гаше (Ницца) с докладом Positivity of the tangent bundle on varieties with trivial canonical class

Аннотация: we all know since Beauville's paper 1983 that smooth projective varieties with trivial canonical class split, after a finite étale covering, as products of an abelian variety, some projective hyperkähler varieties and some Calabi-Yau varieties. Moreover, those three families have very different and rich geometries, which can notably be highlighted through the study of the positivity of their tangent and cotangent bundles, of rational curves on them, of their automorphism groups... An analogous, though even richer picture, holds in the singular setting.

We will discuss why pseudoeffectivity of the tangent bundle of a normal projective terminal variety with trivial canonical class is equivalent to it having an abelian factor in its singular Beauville-Bogomolov decomposition. Then we will sketch a presentation of the tools we use to generalize this statement to normal projective klt varieties, namely orbifold Chern classes.