## Overview

- Provides new results on the arithmetic positivities of Arakelov geometry over adelic curves
- Highlights connections with several classical topics in Arakelov geometry and Diophantine geometry
- Includes detailed proofs and explanations

Part of the book series: Progress in Mathematics (PM, volume 355)

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## About this book

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.

## Keywords

- Arakelov geometry
- adelic curves
- Hilbert-Samuel formula
- adelic line bundle
- arithmetic intersection
- positivity conditions
- Fujita approximation

## Authors and Affiliations

## About the authors

**Huayi Chen** has obtained his doctoral degree in mathematics from Ecole Polytechnique in 2006. He has been associate professor at UniversitĂ© Paris Diderot from 2008 to 2012, professor at UniversitĂ© Grenoble Alpes from 2012 to 2016, and then professor at UniversitĂ© Paris CitĂ© from 2016 to 2023. From 2024, he works at Westlake University as chair professor in mathematics. His research interests include Arakelov geometry, geometry of numbers and convex geometry.

**Atsushi Moriwaki** is a mathematician specializing in algebraic geometry and arithmetic geometry, especially Arakelov geometry. He earned his Ph.D. in Mathematics from Kyoto University in 1991 and went on to serve as a professor at Kyoto University from 2003 to 2023. In 2023, he was appointed as a professor emeritus at Kyoto University and started a new role as a professor at Chubu University.

## Bibliographic Information

Book Title: Positivity in Arakelov Geometry over Adelic Curves

Book Subtitle: Hilbert-Samuel Formula and Equidistribution Theorem

Authors: Huayi Chen, Atsushi Moriwaki

Series Title: Progress in Mathematics

Publisher: BirkhĂ¤user Cham

eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

Hardcover ISBN: 978-3-031-61667-9Due: 12 September 2024

Softcover ISBN: 978-3-031-61670-9Due: 12 September 2024

eBook ISBN: 978-3-031-61668-6Due: 12 September 2024

Series ISSN: 0743-1643

Series E-ISSN: 2296-505X

Edition Number: 1

Number of Pages: X, 178

Number of Illustrations: 7 b/w illustrations