Cubic fourfolds, hyperkähler varieties and one-obstructed Lagrangians

Abstract

Fano fourfolds and compact hyperkähler varieties are two important objects in the study of algebraic geometry. In this talk, we focus on a specific family of Fano fourfolds—cubic fourfolds. Then we investigate their connection with hyperkähler varieties from the perspectives of K3 categories, anti-symplectic involutions and one-obstructed Lagrangians. Besides, we discuss a specific example, the LLSvS eightfold, which serves as an object to illustrate the interplay between the three connections. Furthermore, we briefly recall the proof of Bottini’s work and discuss a possible way of finding atomic Lagrangians of the LLSvS eightfold. This work is still in progress.