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Convergence des polygones de Harder-Narasimhan

Huayi Chen

出版	Société Mathématique de France, 2010
ISBN	28562929689782856292969
URL	http://books.google.com.hk/books?id=lqRIYgEACAAJ&hl=&source=gbs_api

註釋

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.