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Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces: Hyperbolicity in Montréal de Marc-Hubert Nicole

Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces: Hyperbolicity in Montréal: CRM Short Courses

Editat de Marc-Hubert Nicole
en Limba Engleză Paperback – noi 2021
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.
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Specificații

ISBN-13: 9783030498665
ISBN-10: 3030498662
Pagini: 247
Ilustrații: IX, 247 p. 26 illus., 7 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.4 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria CRM Short Courses

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

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

Textul de pe ultima copertă

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.

Caracteristici

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