Combinatorial duality of Hilbert schemes of points in the affine plane

2013/12/31 by Mathias Lederer, Lederer, Mathias
Mathematics · #06A11 #13F20 #13P10 #14C05 #57N80 #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.1401.0179

openalex publication_date 2013/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hilbert scheme of n points in the affine plane contains the open subscheme parametrizing n distinct points in the affine plane, and the closed subscheme parametrizing ideals of codimension n supported at the origin of the affine plane. Both schemes admit Białynicki-Birula decompositions into moduli spaces of ideals with prescribed lexicographic Gröbner deformations. We show that both decompositions are stratifications in the sense that the closure of each stratum is a union of certain other strata. We show that the corresponding two partial orderings on the set of of monomial ideals are dual to each other.

Citations

• Algebraic Families on an Algebraic Surface

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