The Hilbert scheme of points on affine space

The Hilbert scheme of points on affine space

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Burt Totaro, University of California, Los Angeles

Zoom link: https://princeton.zoom.us/j/96282936122

Passcode: 998749

 

I will discuss the Hilbert scheme of d points in affine n-space, with some examples. This is a sort of compactification of the configuration space of d distinct points, but with many mysterious parts: I'll draw some pictures. Nonetheless, we determine the homotopy type of the Hilbert scheme in a range of dimensions. Many questions remain.

Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.