| Résume | It is a standard theme in [algebraic] geometry to define classes of mild singularities for which certain properties that hold in the smooth case extend. The typical example of such mild singularities are the rational and Du Bois singularities (from a cohomological point of view) and canonical and log canonical singularities (from an MMP point of view). In this talk. I will discuss the notions of higher rational and higher Du Bois, which generalize these standard concepts. (Here, higher=milder!) I will discuss the Hodge theoretic motivation for such, as well as a geometric application to the moduli theory of Calabi-Yau varieties. Time permitting, I will specialize to the isolated singularity case, where everything becomes more transparent, and expressible in terms of standard invariants of singularities. |
