Wed, 05 Jun 2024
17:00
17:00
C4
Hilbert-Burch matrices and points on a plane
Piotr Oszer
(University of Warsaw)
Abstract
The Hilbert scheme of d-points on a smooth surface is a well-studied object that still enjoys relatively large interest. We generalize Aldo Conca's Canonical Hilbert-Burch matrices and obtain explicit families of d-points. We show that such descriptions give us Białynicki-Birula cells of the Hilbert scheme for any choice of one-dimensional torus, thus describing the punctual component. This can be potentially applied to the study of singularities of the nested Hilbert scheme of points.
