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Relevant bibliographies by topics / Formule de Hilbert-Samuel

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Academic literature on the topic 'Formule de Hilbert-Samuel'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Formule de Hilbert-Samuel"

1

Enescu, Florian, and Sandra Spiroff. "Computing the invariants of intersection algebras of principal monomial ideals." International Journal of Algebra and Computation 29, no. 02 (March 2019): 309–32. http://dx.doi.org/10.1142/s0218196719500036.

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We continue the study of intersection algebras [Formula: see text] of two ideals [Formula: see text] in a commutative Noetherian ring [Formula: see text]. In particular, we exploit the semigroup ring and toric structures in order to calculate various invariants of the intersection algebra when [Formula: see text] is a polynomial ring over a field and [Formula: see text] are principal monomial ideals. Specifically, we calculate the [Formula: see text]-signature, divisor class group, and Hilbert–Samuel and Hilbert–Kunz multiplicities, sometimes restricting to certain cases in order to obtain explicit formulæ. This provides a new class of rings where formulæ for the [Formula: see text]-signature and Hilbert–Kunz multiplicity, dependent on families of parameters, are provided.

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2

Yuan, Xinyi, and Tong Zhang. "Effective bounds of linear series on algebraic varieties and arithmetic varieties." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 736 (March 1, 2018): 255–84. http://dx.doi.org/10.1515/crelle-2015-0025.

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AbstractIn this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes. They are effective versions of the Hilbert–Samuel formula and the arithmetic Hilbert–Samuel formula. The treatments are high-dimensional generalizations of [25] and [26]. Similar results are obtained independently by Huayi Chen [7] with less explicit error terms.

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3

Dichi, H., and D. Sangare. "Hilbert–Samuel functions of well bifiltered modules." Asian-European Journal of Mathematics 09, no. 02 (April 15, 2016): 1650031. http://dx.doi.org/10.1142/s1793557116500315.

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In an earlier paper, we studied the Hilbert quasi-polynomial functions of finitely generated bigraded modules in the general framework when the base ring is bigraded and generated by finitely many homogeneous elements of arbitrary degrees. In this paper, we introduce the concept of [Formula: see text]-good bifiltration [Formula: see text] on a finitely generated [Formula: see text]-module [Formula: see text], where [Formula: see text] and [Formula: see text] are specified noetherian filtrations on the noetherian ring [Formula: see text]. The bigraded modules associated with such bifiltrations are shown to be finitely generated under reasonable hypotheses. Their Hilbert functions are studied. The Hilbert–Samuel function of [Formula: see text] with respect to the [Formula: see text]-good bifiltration [Formula: see text] of [Formula: see text] is one of them. It is proved, among others, that this function is a quasi-polynomial function in two variables and that if [Formula: see text] is a noetherian local ring and if the filtrations [Formula: see text] and [Formula: see text] are primary filtrations, then its degree equals the Krull dimension of [Formula: see text].

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4

Jorge Pérez, V. H., and T. H. Freitas. "Hilbert–Samuel multiplicity and Northcott’s inequality relative to an Artinian module." International Journal of Algebra and Computation 30, no. 02 (October 24, 2019): 379–96. http://dx.doi.org/10.1142/s0218196720500034.

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Let [Formula: see text] be a commutative quasi-local ring (with identity [Formula: see text]), and let [Formula: see text] be an [Formula: see text]-ideal such that [Formula: see text]. For [Formula: see text] an Artinian [Formula: see text]-module of N-dimension [Formula: see text], we introduce the notion of Hilbert-coefficients of [Formula: see text] relative to [Formula: see text] and give several properties. When [Formula: see text] is a co-Cohen–Macaulay [Formula: see text]-module, we establish the Northcott’s inequality for Artinian modules. As applications, we show some formulas involving the Hilbert coefficients and we investigate the behavior of these multiplicities when the module is the local cohomology module.

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5

Crabbe, Andrew, Daniel Katz, Janet Striuli, and Emanoil Theodorescu. "Hilbert-Samuel polynomials for the contravariant extension functor." Nagoya Mathematical Journal 198 (June 2010): 1–22. http://dx.doi.org/10.1017/s0027763000009910.

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AbstractLet(R,m)be a local ring, and letMandNbe finiteR-modules. In this paper we give a formula for the degree of the polynomial giving the lengths of the modules ExtiR(M,N/mnN). A number of corollaries are given, and more general filtrations are also considered.

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6

Crabbe, Andrew, Daniel Katz, Janet Striuli, and Emanoil Theodorescu. "Hilbert-Samuel polynomials for the contravariant extension functor." Nagoya Mathematical Journal 198 (June 2010): 1–22. http://dx.doi.org/10.1215/00277630-2009-005.

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AbstractLet (R,m) be a local ring, and let M and N be finite R-modules. In this paper we give a formula for the degree of the polynomial giving the lengths of the modules ExtiR(M,N/mnN). A number of corollaries are given, and more general filtrations are also considered.

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7

Cheng, Guozheng, and Xiang Fang. "An additive formula for Samuel multiplicities on Hilbert spaces of analytic functions." Journal of Functional Analysis 260, no. 7 (April 2011): 2027–42. http://dx.doi.org/10.1016/j.jfa.2010.09.015.

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8

MAGNÚSSON, JÓN I., ALEXANDER RASHKOVSKII, RAGNAR SIGURDSSON, and PASCAL J. THOMAS. "LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS." International Journal of Mathematics 23, no. 06 (May 6, 2012): 1250065. http://dx.doi.org/10.1142/s0129167x12500656.

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Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Sε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each Sε we associate its vanishing ideal [Formula: see text] and pluricomplex Green function [Formula: see text]. Suppose that, as ε tends to 0, [Formula: see text] converges to [Formula: see text] (local uniform convergence), and that (Gε)ε converges to G, locally uniformly away from 0; then [Formula: see text]. If the Hilbert–Samuel multiplicity of [Formula: see text] is strictly larger than its length (codimension, equal to N here), then (Gε)ε cannot converge to [Formula: see text]. Conversely, if [Formula: see text] is a complete intersection ideal, then (Gε)ε converges to [Formula: see text]. We work out the case of three poles.

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9

Botero, Ana María, and José Ignacio Burgos Gil. "Toroidal b-divisors and Monge–Ampère measures." Mathematische Zeitschrift, June 24, 2021. http://dx.doi.org/10.1007/s00209-021-02789-5.

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AbstractWe generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of nef b-divisors on complete varieties which are toroidal with respect to a snc divisor. As a key ingredient we show the existence of a limit measure, supported on a balanced rational conical polyhedral space attached to the toroidal embedding, which arises as a limit of discrete measures defined via tropical intersection theory on the polyhedral space. We prove that the intersection theory of nef Cartier b-divisors can be extended continuously to nef toroidal Weil b-divisors and that their degree can be computed as an integral with respect to this limit measure. As an application, we show that a Hilbert–Samuel type formula holds for big and nef toroidal Weil b-divisors.

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Dissertations / Theses on the topic "Formule de Hilbert-Samuel"

1

Randriambololona, Hugues. "Hauteurs pour les sous-schémas et exemples d'utilisation de méthodes arakeloviennes en théorie de l'approximation diophantienne." Phd thesis, Université Paris Sud - Paris XI, 2002. http://tel.archives-ouvertes.fr/tel-00359859.

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Dans cette thèse on définit et étudie un certain nombre de notions dans le cadre de la géométrie d'Arakelov qui, d'une part, possèdent un intérêt intrinsèque et, d'autre part, sont susceptibles d'applications à la théorie de l'approximation diophantienne.

La plus grande partie du texte est consacrée à l'élaboration d'une théorie des hauteurs pour les sous-schémas et à la preuve de «formules de Hilbert-Samuel» pour ces hauteurs. Pour deux classes importantes de sous-schémas (les sous-schémas intègres et les sous-schémas «lisses avec multiplicités») on montre que la hauteur du sous-schéma relativement à une grande puissance d'un fibré en droites positif est asymptotiquement déterminée par la hauteur du cycle associé. La démonstration repose essentiellement sur le «théorème de Hilbert-Samuel arithmétique» de Gillet et Soulé, auquel elle se ramène par l'utilisation de techniques de géométrie analytique hermitienne. On fait ensuite une analyse plus fine du développement asymptotique des hauteurs de certains sous-schémas particuliers. Notamment, dans le cas de la dimension relative zéro, on exprime le terme constant du développement asymptotique en fonction de la ramification du sous-schéma, ce qui résout une question de Michel Laurent sur les hauteurs des matrices d'interpolation.

Enfin, dans une partie indépendante, on expose diverses applications de méthodes arakeloviennes à des problèmes d'approximation diophantienne. En particulier on donne une nouvelle démonstration d'un critère classique d'indépendance algébrique dont l'originalité est qu'elle n'utilise plus de théorie de l'élimination mais uniquement des techniques de théorie de l'intersection arithmétique.

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