The Hilbert scheme of points on 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 has been poorly understood. For n greater than d, we determine the homotopy type of the Hilbert scheme in a range of dimensions. The proof uses the homotopy theory of algebraic stacks. Many questions remain. (Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.)

algebraic geometrygroup theorynumber theoryrepresentation theory

Audience: researchers in the topic

Algebraic groups and algebraic geometry: in honor of Zinovy Reichstein's 60th birthday