The Hilbert scheme of infinite affine space

Abstract: I will discuss the Hilbert scheme of $d$ points in affine $n$-space, with some examples. This space has many irreducible components for $n$ at least 3 and is poorly understood. Nonetheless, in the limit where $n$ goes to infinity, we show that the Hilbert scheme of $d$ points in infinite affine space has a very simple homotopy type. In fact, it has the $A^1$-homotopy type of the infinite Grassmannian $BGL(d-1)$. Many questions remain. (Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.)

algebraic geometryalgebraic topologyK-theory and homology

Audience: researchers in the topic

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com