The variety of polar simplices II

Joachim Jelisiejew; Kristian Ranestad; Frank-Olaf Schreyer

The variety of polar simplices II

Algebraic Geometry 2024-04-09 v2 Commutative Algebra

Authors: Joachim Jelisiejew , Kristian Ranestad , Frank-Olaf Schreyer

Abstract

We discuss the space $VPS(Q,H)$ of ideals with Hilbert function $H=(1,n,n, \ldots)$ that are apolar to a full rank quadric $Q$ . We prove that its components of saturated ideals are closely related to the locus of Gorenstein algebras and to the Slip component in border apolarity. We also point out an important error in~[RS] and provide the necessary corrections.

Keywords

polar simplices apolar ideals hilbert function gorenstein algebras border apolarity quadric

Cite

@article{arxiv.2304.00533,
  title  = {The variety of polar simplices II},
  author = {Joachim Jelisiejew and Kristian Ranestad and Frank-Olaf Schreyer},
  journal= {arXiv preprint arXiv:2304.00533},
  year   = {2024}
}

Comments

version 2, final, to appear in Experimental Math

The variety of polar simplices II

Abstract

Keywords

Cite

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