Identifying limits of ideals of points in the case of projective space
Algebraic Geometry
2021-12-01 v2
Abstract
We study the closure of the locus of radical ideals in the multigraded Hilbert scheme associated with a standard graded polynomial ring and the Hilbert function of a homogeneous coordinate ring of points in general position in projective space. In the case of projective plane, we give a sufficient condition for an ideal to be in the closure of the locus of radical ideals. For projective space of arbitrary dimension we present a necessary condition. The paper is motivated by the border apolarity lemma which connects such multigraded Hilbert schemes with the theory of ranks of polynomials.
Keywords
Cite
@article{arxiv.2011.14692,
title = {Identifying limits of ideals of points in the case of projective space},
author = {Tomasz Mańdziuk},
journal= {arXiv preprint arXiv:2011.14692},
year = {2021}
}
Comments
Final version published in Linear Algebra and its Applications