Rational Curves on Algebraic Varieties

Authors: Lütkebohmert, Werner
The first comprehensive presentation of the whole topic of curves, Jacobians, abelian varieties and proper analytic group varieties over non-archimedian fields
Introduces the powerful tools of formal algebraic geometry as used in arithmetic geometry
The book builds a bridge to the more advanced research on the moduli of degeneration of abelian varieties which is a central object in arithmetic geometry

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems.