Quantitative Arithmetic of Projective Varieties

• Main Author: Browning, Timothy D. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Birkhũser Basel, 2009.
• Series: Progress in Mathematics ; 277
• Subjects: Mathematics.; Global differential geometry.; Number theory.; Number Theory.; Differential Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0346-0129-0

This monograph is concerned with counting rational points of bounded height on projective algebraic varieties. This is a relatively young topic, whose exploration has already uncovered a rich seam of mathematics situated at the interface of analytic number theory and Diophantine geometry. The goal o...

Table of Contents:

• Preface
• 1. Introduction
• 2. The Manin Conjectures
• 3. The Dimension Growth Conjecture
• 4. Uniform Bounds for Curves and Surfaces
• 5. A1 Del Pezzo Surface of Degree 6
• 6. D4 Del Pezzo Surface of Degree 3
• 7. Siegel's Lemma and Non-singular Surfaces
• 8. The Hardy-Littlewood Circle Method
• Bibliography
• Index.