Abstract: The rationality problem for cubic fourfolds is a long-standing question, closely related to the study of the Hodge loci in the moduli space C of such varieties. Katzarkov, Kontsevich, Pantev, and Yu recently proved that a very general cubic fourfold is not rational, in accordance with Kuznetsov’s conjecture, which predicts that the rational ones lie in the union of certain special divisors contained in the Hodge locus of C. Some examples of smooth rational and irrational cubic fourfolds are known, but the geometry of C is still largely unexplored. It is therefore interesting to study nonspecial divisors in C: in this talk we briefly present the known ones, with particular focus on the ones we constructed, whose union is called Severi divisor.

 

Link Information: https://us02web.zoom.us/j/81933757305?pwd=cStESHpoMDhUelVKeDd1bUlIZmVZZz09

 

Organizer: Sasha Viktorova (NCTS)