Local finite dimensional Gorenstein k-algebras having Hilbert function (1,5,5,1) are smoothable

2012/12/03 by Jelisiejew, Joachim
#13D10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.0522

Abstract

Let k be an algebraically closed field of characteristic 0. The question of irreducibility of the punctual Hilbert scheme Hilb_d Pⁿ and its Gorenstein locus for various d was studied in [CEVV8, CN9, CN10, CN11]. In this short paper we prove that the subschemes corresponding to the Gorenstein algebras having Hilbert function (1,5,5,1) are smoothable i.e. lie in the closure of the locus of smooth subschemes. Among the Gorenstein algebras of length 12 the smoothability of algebras having such Hilbert function seems to be the most inapproachable using non-direct tools e.g. structural theorems.

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