Birational Geometry and Manin's Conjecture

This book provides the first comprehensive study of the geometric aspects of Manin's conjecture. It equips the reader with a working knowledge of higher dimensional algebraic geometry, including the minimal model program and its applications to arithmetic and Diophantine geometry. The text also develops the foundations of the moduli theory of rational curves on Fano varieties and explores its role in the geometric formulation of Manin's conjecture, supported by worked examples. The book is suitable for graduates and researchers in arithmetic geometry seeking a modern introduction to birational geometry and the moduli theory of rational curves. It will also interest experts in higher-dimensional algebraic geometry who wish to understand recent applications of these techniques to arithmetic geometry.