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Positivity in Arakelov geometry over...

Chen, Huayi.

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Positivity in Arakelov geometry over Adelic curves = Hilbert-Samuel formula and equidistribution theorem /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Positivity in Arakelov geometry over Adelic curves/ by Huayi Chen, Atsushi Moriwaki.
Reminder of title:	Hilbert-Samuel formula and equidistribution theorem /
Author:	Chen, Huayi.
other author:	Moriwaki, Atsushi.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	viii, 251 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Review and Preliminaries -- Normed Graded Linear Series over a Trivially Valued Field -- Arithmetic Volumes over a General Adelic Curve -- Hilbert-Samuel Property -- Relative Ampleness and Nefness -- Global Adelic Space of an Arithmetic Variety -- Generically Big and Pseudo-effective Adelic Line Bundles -- Global Positivity Conditions -- Appendix A: Some Slope Estimates.
Contained By:	Springer Nature eBook
Subject:	Arakelov theory. -
Online resource:	https://doi.org/10.1007/978-3-031-61668-6
ISBN:	9783031616686

Positivity in Arakelov geometry over Adelic curves = Hilbert-Samuel formula and equidistribution theorem /
Chen, Huayi.

Positivity in Arakelov geometry over Adelic curvesHilbert-Samuel formula and equidistribution theorem /[electronic resource] :by Huayi Chen, Atsushi Moriwaki. - Cham :Springer Nature Switzerland :2024. - viii, 251 p. :ill., digital ;24 cm. - Progress in mathematics,v. 3552296-505X ;. - Progress in mathematics ;v. 355..

Introduction -- Review and Preliminaries -- Normed Graded Linear Series over a Trivially Valued Field -- Arithmetic Volumes over a General Adelic Curve -- Hilbert-Samuel Property -- Relative Ampleness and Nefness -- Global Adelic Space of an Arithmetic Variety -- Generically Big and Pseudo-effective Adelic Line Bundles -- Global Positivity Conditions -- Appendix A: Some Slope Estimates.

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.

ISBN: 9783031616686

Standard No.: 10.1007/978-3-031-61668-6doiSubjects--Topical Terms:

728392
Arakelov theory.

LC Class. No.: QA242.6

Dewey Class. No.: 516.35

Positivity in Arakelov geometry over Adelic curves = Hilbert-Samuel formula and equidistribution theorem /
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505 0 $a Introduction -- Review and Preliminaries -- Normed Graded Linear Series over a Trivially Valued Field -- Arithmetic Volumes over a General Adelic Curve -- Hilbert-Samuel Property -- Relative Ampleness and Nefness -- Global Adelic Space of an Arithmetic Variety -- Generically Big and Pseudo-effective Adelic Line Bundles -- Global Positivity Conditions -- Appendix A: Some Slope Estimates.
520 $a 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.
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