Abstract
ABSTRACTIn 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.
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