Overview
- Introduces a number of exciting developments and cutting-edge results related to hyperbolicity, and the fundamental conjectures of Ax–Schanuel, Bombieri, Campana, Lang, Vojta, and others
- Features chapters written by leading experts in their areas, collecting many of their own recent advances
- Motivates a range of readers by presenting each chapter’s respective material in a self-contained and accessible manner
Part of the book series: CRM Short Courses (CRMSC)
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About this book
- The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures;
- A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective;
- A systematic presentation and comparison between different notions of hyperbolicity,as an introduction to the Lang–Vojta conjectures in the projective case;
- An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties.
Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.
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Keywords
- Hyperbolicity
- Moduli spaces
- Logarithmic pairs
- Bombieri-Lang conjecture
- Faltings theorem
- o-minimal geometry
- Ax-Schanuel theorem
- Ax-Schanuel conjecture
- Hodge theory
- Orbifold pairs
- Campana conjectures
- Lang-Vojta conjectures
- Log general type
- Number theory
- Brody hyperbolicity
- Algebraic hyperbolicity
- Kodaira dimension
Table of contents (4 chapters)
Editors and Affiliations
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Bibliographic Information
Book Title: Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces
Book Subtitle: Hyperbolicity in Montréal
Editors: Marc-Hubert Nicole
Series Title: CRM Short Courses
DOI: https://doi.org/10.1007/978-3-030-49864-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-49863-4Published: 01 November 2020
Softcover ISBN: 978-3-030-49866-5Published: 01 November 2021
eBook ISBN: 978-3-030-49864-1Published: 31 October 2020
Series ISSN: 2522-5200
Series E-ISSN: 2522-5219
Edition Number: 1
Number of Pages: IX, 247
Number of Illustrations: 19 b/w illustrations, 7 illustrations in colour
Topics: Algebraic Geometry, Number Theory