Irreducibility of the Gorenstein locus of the punctual Hilbert scheme of\n degree 10

2010/03/29 by Gianfranco Casnati, Casnati, Gianfranco, Roberto Notari +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1003.5569

openalex publication_date 2010/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of characteristic 0 and let\nH_G(d,N) be the open locus of the Hilbert scheme H(d,N) corresponding to\nGorenstein subschemes of degree d in the projective N-space. We proved in a\nprevious paper that H_G(d,N) is irreducible for d\≤9 and N\≥1. In the\npresent paper we prove that also H_G(10,N) is irreducible for each N\≥1,\ngiving also a complete description of its singular locus.\n

Citations

• Algebraic Families on an Algebraic Surface
• Isomorphism classes of certain Artinian Gorenstein algebras

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