Solution of a conjecture of C. Berenstein - A. Yger and invariants of contact at infinity

DOI10.5802/aif.1834zbMath0991.13009OpenAlexW2316497077WikidataQ123264305 ScholiaQ123264305MaRDI QIDQ5936665

Michel Hickel

Publication date: 4 July 2001

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2001__51_3_707_0

zbMATH Keywords

Bézout theoremintegral representationintersection theoryintegral closure of idealseffective Nullstellensatzglobal Łojasiewicz inequalities

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15) Power series, series of functions of several complex variables (32A05) Analytic spaces (32C99) Relevant commutative algebra (14A05)

Related Items (14)

The membership problem for polynomial ideals in terms of residue currents ⋮ Averaging Residue Currents and the Stückrad–Vogel Algorithm ⋮ Variants of the Effective Nullstellensatz and Residue Calculus ⋮ Division formulas on projective varieties ⋮ An Effective Uniform Artin–Rees Lemma ⋮ Explicit representation of membership in polynomial ideals ⋮ Some variants of Macaulay's and Max Noether's theorems ⋮ Sparse effective membership problems via residue currents ⋮ Analytic residues along algebraic cycles ⋮ Flexibility of analysis serving computational polynomial algebra or arithmetics ⋮ Integral closure of ideals and equisingularity ⋮ Bounds for multivariate residues and for the polynomials in the elimination theorem ⋮ Residue currents of holomorphic morphisms ⋮ Global effective versions of the Briançon-Skoda-Huneke theorem

Cites Work

• Bounds for the degrees in the division problem
• Bounds for the degrees in the Nullstellensatz
• Jacobian ideals and a theorem of Briancon-Skoda
• Variétés polaires. I: Invariants polaires des singularites d'hypersurfaces
• Pseudo-rational local rings and a theorem of Briancon-Skoda about integral closures of ideals
• Separation of algebraic sets and the Łojasiewicz exponent of polynomial mappings
• A geometric effective Nullstellensatz
• A pure power product version of the Hilbert Nullstellensatz
• The complexity of the word problems for commutative semigroups and polynomial ideals
• Effective Nullstellensatz for arbitrary ideals
• Some asymptotic properties of powers of ideals
• A Global Lojasiewicz Inequality for Algebraic Varieties
• Residue calculus and effective Nullstellensatz
• Fonction de Artin et Germes de Courbes Tracees sur un Germe D'Espace Analytique
• Sharp Effective Nullstellensatz
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