On the Hilbert schemes of finite algebras over an algebraically closed field

In this paper, we study properties of the Hilbert schemes of ideals of finite algebras over an algebraically closed field. We prove a duality theorem for the Hilbert schemes of a finite Gorenstein algebra. We also study some properties of finite algebras obtained from informations on their Hilbert s...

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Bibliographic Details
Published in:Communications in algebra 2018-06, Vol.46 (6), p.2753-2765
Main Author: Matsuzawa, Yohsuke
Format: Article
Language:English
Subjects:
Algebra
Combinatorial analysis
Duality theorem
Finite algebras
Hilbert schemes
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Summary:In this paper, we study properties of the Hilbert schemes of ideals of finite algebras over an algebraically closed field. We prove a duality theorem for the Hilbert schemes of a finite Gorenstein algebra. We also study some properties of finite algebras obtained from informations on their Hilbert schemes. We give examples of finite algebras A such that the sequences are unimodal. They are examples of a generalization of a combinatorial conjecture by Stanton.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2017.1399409