Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces
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Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces
Author: Marc-Hubert Nicole
language: en
Publisher: Springer Nature
Release Date: 2020-10-31
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.
Point-Counting and the Zilber–Pink Conjecture
Author: Jonathan Pila
language: en
Publisher: Cambridge University Press
Release Date: 2022-06-09
Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.
Algebraic Geometry
Author: Dan Abramovich
language: en
Publisher: American Mathematical Soc.
Release Date: 2009
Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.