Hilbert schemes of finite abelian group orbits and Grobner fans

2007/12/18 by Tomohito Morita, Morita, Tomohito
Computer Science · Mathematics · #13P10 #14E15 #14L30 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0712.2892

openalex publication_date 2007/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite abelian subgroup of PGL(r-1,K)=Aut(¶^r-1_K). In this paper, we prove that the normalization of the G-orbit Hilbert scheme \Hilb^G(¶^r-1) is described as a toric variety, which corresponds to the Gröbner fan for some homogeneous ideal I of K[x₁, ..., x_r].

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