Colloquium: Cubic fourfolds and their Fano varieties of lines

Abstract: Identifying which cubic fourfolds are rational is a famous open problem in classical algebraic geometry. It has been approached from numerous perspectives, one of which is using the variety parametrizing lines on the cubic fourfold, called the Fano variety of lines. There is a natural relationship between the geometry of a cubic fourfold and of its Fano variety of lines, but a better understanding of this relationship is expected to shed light on the birational geometry of cubic fourfolds. In this talk, I will discuss joint work with C. Brooke and L. Marquand, in which we investigate this circle of ideas. 

Host: John Shareshian