Hilbert schemes, commuting matrices, and hyperk\"ahler geometry
Algebraic Geometry
2021-11-11 v8 Differential Geometry
Abstract
We represent algebraic curves via commuting matrix polynomials. This allows us to show that the Hilbert scheme of cohomologically stable twisted rational curves of degree in is isomorphic to a complexified hyperk\"ahler quotient of an open subset of a vector space by a non-reductive Lie group.
Cite
@article{arxiv.1903.01836,
title = {Hilbert schemes, commuting matrices, and hyperk\"ahler geometry},
author = {Roger Bielawski and Carolin Peternell},
journal= {arXiv preprint arXiv:1903.01836},
year = {2021}
}
Comments
References added; presentation improved; minor corrections. To appear in the Journal of the LMS. ${}$