The Variety of Polar Simplices II

We discuss the space VPS(Q, H) of ideals with Hilbert function H=(1,n,n,…) 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...

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Published in:Experimental mathematics 2024-04, p.1-33
Main Authors: Jelisiejew, Joachim, Ranestad, Kristian, Schreyer, Frank-Olaf
Format: Article
Language:English
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Summary:We discuss the space VPS(Q, H) of ideals with Hilbert function H=(1,n,n,…) 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 [Citation20] and provide the necessary corrections.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2024.2343846