Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces

Hyperbolicity in Montréal

Buch | Softcover

IX, 247 Seiten

2021 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-49866-5 (ISBN)

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This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes:

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.

lt;b>Marc-Hubert Nicole is a professor of mathematics in the French university system.

Lectures on the Ax-Schanuel Conjecture.- Arithmetic Aspects of Orbifold Pairs.- The Lang-Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties.- Hyperbolicity of Varieties of Log General Type.

Erscheinungsdatum	02.11.2021
Reihe/Serie	CRM Short Courses
Zusatzinfo	IX, 247 p. 26 illus., 7 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	403 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebraic hyperbolicity • Ax-Schanuel conjecture • Ax-Schanuel theorem • Bombieri-Lang conjecture • Brody hyperbolicity • Campana conjectures • Faltings theorem • Hodge Theory • hyperbolicity • Kodaira Dimension • Lang-Vojta conjectures • Logarithmic pairs • Log general type • moduli spaces • Number Theory • o-minimal geometry • Orbifold pairs
ISBN-10	3-030-49866-2 / 3030498662
ISBN-13	978-3-030-49866-5 / 9783030498665
Zustand	Neuware