English

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