Geometric Consequences of Extremal Behavior in a Theorem of Macaulay

DOI10.2307/2154949zbMath0820.13019OpenAlexW4246119846MaRDI QIDQ4321192

Anthony V. Geramita, Anna Maria Bigatti, Juan C. Migliore

Publication date: 9 July 1995

Full work available at URL: https://doi.org/10.2307/2154949

zbMATH Keywords

uniformityHilbert functionszero-schemespoints in uniform position

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Schemes and morphisms (14A15)

Related Items (38)

N-TYPE VECTORS AND THE CAYLEY-BACHARACH PROPERTY ⋮ On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four ⋮ On zero-dimensional subschemes of a complete intersections ⋮ Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz ⋮ The strength of the weak Lefschetz property ⋮ Some geometric results arising from the Borel fixed property ⋮ Green's theorem and Gorenstein sequences ⋮ Distinguishing \(\Bbbk\)-configurations ⋮ On the identifiability of ternary forms ⋮ Generic initial ideals and graded Artinian-level algebras not having the weak-Lefschetz property ⋮ The unimodality of pure \(O\)-sequences of type three in three variables ⋮ Effective Criteria for Specific Identifiability of Tensors and Forms ⋮ On the weak Lefschetz property for height four equigenerated complete intersections ⋮ Generic local rings on a spectrum between Golod and Gorenstein ⋮ On the Hilbert functions of sets of points in ¹ × ¹ × ¹ ⋮ Complete intersections on Veronese surfaces ⋮ Some special configurations of points in \(\mathbb P^n\) ⋮ On the uniformity of zero-dimensional complete intersections ⋮ Extremal behavior in sectional matrices ⋮ Growth conditions for a family of ideals containing regular sequences ⋮ On a geometric method for the identifiability of forms ⋮ Some algebraic consequences of Green's hyperplane restriction theorems ⋮ Hilbert functions and level algebras ⋮ Hilbert functions on Cohen-Macaulay ideals with assigned generators' degrees ⋮ A new approach to the Hilbert function of a 0-dimensional projective scheme ⋮ Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces ⋮ Hilbert functions of schemes of double and reduced points ⋮ The weak and strong Lefschetz properties for Artinian \(K\)-algebras ⋮ Classifying Hilbert functions of fat point subschemes in \(\mathbb{P}^2\) ⋮ The Gotzmann coefficients of Hilbert functions ⋮ Stanley’s nonunimodal Gorenstein $h$-vector is optimal ⋮ Green and Gotzmann theorems for polynomial rings with restricted powers of the variables ⋮ Curves and their hyperplane sections ⋮ Line arrangements and configurations of points with an unexpected geometric property ⋮ Sets of points which project to complete intersections, and unexpected cones ⋮ Progress on the symmetric Strassen conjecture ⋮ Almost maximal growth of the Hilbert function ⋮ Minimality and uniqueness for decompositions of specific ternary forms

Cites Work

• The ideal of forms vanishing at a finite set of points in \({\mathbb{P}}^ n\)
• On a theorem of Castelnuovo, and the equations defining space curves
• Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes
• Hilbert functions of graded algebras
• The Hilbert Function of a Reduced K -Algebra
• Lectures on Curves on an Algebraic Surface. (AM-59)
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