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Convergence des Polygones de Harder-Narasimhan
Huayi Chen, Université Paris Diderot, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
2010; 120 pp; softcover
Number: 120
ISBN-10: 2-85629-296-8
ISBN-13: 978-2-85629-296-9
List Price: US$42
Member Price: US$33.60
Order Code: SMFMEM/120
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The author interprets the theory of Harder-Narasimhan polygons by the language of \(\mathbb R\)-filtrations. By using a variant version of Fekete's lemma and a combinatoric argument on monomials, he establishes the uniform convergence of polygons associated to a graded algebra equipped with filtrations. This leads to the existence of several arithmetic invariants, a very particular case of which is the sectional capacity. Two applications in Arakelov geometry are developed: the arithmetic Hilbert-Samuel theorem and the existence and the geometric interpretation of the asymptotic maximal slope.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

  • Introduction
  • Rappels et préliminaires
  • Filtrations de Harder-Narasimhan
  • Convergence des polygones
  • Applications
  • Bibliographie
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