In this talk, we will introduce the coregularity of Fano varieties.
This invariant measures how large of a dual complex can we find among log Calabi-Yau structures on a Fano variety. The coregularity relates to log canonical thresholds, existence of complements, and the index of log Calabi-Yau pairs. In this talk, we will discuss some recent results about this invariant and other future directions. The results of this talk are joint work with Fernando Figueroa, Stefano Filipazzi, Mirko Mauri, and Junyao Peng.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
