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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 A1-homotopy type of the infinite Grassmannian BGL(d1). Many questions remain. (Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.)

This talk is hosted by Stanford University. Link to the talk site.