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 AxSchanuel 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 LangVojta conjectures in the projective case;
• An exploration of hyperbolicity and the LangVojta 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.

Introduces a number of exciting developments and cutting-edge results related to hyperbolicity, and the fundamental conjectures of AxSchanuel, 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

Autorentext

Marc-Hubert Nicole is a professor of mathematics in the French university system.

Inhalt
Lectures on the AxSchanuel Conjecture.- Arithmetic Aspects of Orbifold Pairs.- The LangVojta Conjectures on Projective Pseudo-Hyperbolic Varieties.- Hyperbolicity of Varieties of Log General Type.