Michael Stillman: The combinatorial structure of Quot schemes on projective space: which are smooth?

Abstract:

Hilbert schemes parametrize subschemes of projective space with a fixed Hilbert polynomial. Quot schemes are a generalization where we consider quotients of a coherent sheaf with a fixed Hilbert polynomial.

In this talk, our main focus is to determine for those Quot schemes parametrizing quotients of a sum of copies of the structure sheaf on projective space, which are smooth? Along the way, we will describe combinatorial and computational algebra tools that help us solve this problem. We will also describe interesting examples of Quot schemes which are not smooth.

This represents very recent joint work with Roy Skjelnes and Greg Smith.