Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces

1. Front Matter

   Pages i-ix

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2. Lectures on the Ax–Schanuel conjecture

   • Benjamin Bakker, Jacob Tsimerman

   Pages 1-68

3. Arithmetic Aspects of Orbifold Pairs

   • Frédéric Campana

   Pages 69-133

4. The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties

   • Ariyan Javanpeykar

   Pages 135-196

5. Hyperbolicity of Varieties of Log General Type

   • Kenneth Ascher, Amos Turchet

   Pages 197-247

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.

• 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

• Institut de mathématiques de Marseille (I2M), Université d’ Aix-Marseille, Marseille, France

  Marc-Hubert Nicole

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

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