Positivity in Arakelov Geometry over Adelic Curves

Hilbert-Samuel Formula and Equidistribution Theorem

von Huayi Chen, Atsushi Moriwaki

251 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors. It explores positivity conditions and establishes the Hilbert-Samuel formula and the equidistribution theorem in the context of adelic curves. Connections with several classical topics in Arakelov geometry and Diophantine geometry are highlighted, such as the arithmetic Hilbert-Samuel formula, positivity of line bundles, equidistribution of small subvarieties, and theorems resembling the Bogomolov conjecture. Detailed proofs and explanations are provided to ensure the text is accessible to both graduate students and experienced researchers.

• Reihe: Progress in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Geometrie Algebraische Geometrie
• ISBN: 9783031616709
• Sprache: Englisch
• Erscheinungsdatum: 23.08.2025
• Größe: 23.5 x 15.5 cm
• Verlag: Springer International Publishing