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OverviewThe main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry, i.e., the study of big linear series on algebraic varieties. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties. The book includes such fundamental results as arithmetic Hilbert-Samuel formula, arithmetic Nakai-Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang-Bogomolov conjecture and so on. In addition, the author presents, with full details, the proof of Faltings' Riemann-Roch theorem. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes. Full Product DetailsAuthor: Atsushi MoriwakiPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 244 Weight: 0.680kg ISBN: 9781470410742ISBN 10: 1470410745 Pages: 285 Publication Date: 30 December 2014 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreliminariesGeometry of numbersArakelov geometry on arithmetic curvesArakelov geometry on arithmetic surfacesArakelov geometry on general arithmetic varietiesArithmetic volume function and its continuityNakai-Moishezon criterion on an arithmetic varietyArithmetic Bogomolov inequalityLang-Bogomolov conjectureBibliographyIndexReviewsAuthor InformationAtsushi Moriwaki, Kyoto University, Japan. Tab Content 6Author Website:Countries AvailableAll regions |
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