Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: The Hilbert scheme of a pair of linear spaces and Mori dream spaces

Seminar | October 30 | 3:45-4:45 p.m. | 939 Evans Hall

 Ritvik Ramkumar, UC Berkeley

 Department of Mathematics

The Grassmannian is a smooth moduli space with very rich geometry that parameterizes simple varieties, namely linear spaces. One can study a "natural" generalization, the component of a Hilbert scheme that parameterizes a pair of linear spaces in $\mathbb P^n$. In this talk we will describe a powerful rigidity result that allows us to completely control degenerations in this component. We will then use it to give new examples of smooth components and show that they are Mori dream spaces. Time permitting, we will discuss the other cases that we are currently working out. This is a work in progress.