Birational geometry and Manin's conjecture / Sho Tanimoto

Format:

Book

Author/Creator:

Tanimoto, Shō, author.

Series:

Cambridge tracts in mathematics ; 237.

Cambridge tracts in mathematics ; 237

Language:

English

Subjects (All):

Geometry, Algebraic.

Physical Description:

1 online resource

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"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"-- Cambridge Core

Contents:

Height functions

A brief introduction to higher dimensional algebraic geometry

Manin’s conjecture

Proofs of main results

Further examples

Moduli of rational curves

Examples of geometric Manin’s conjecture II

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed July 13, 2026)

Other Format:

Print version: Tanimoto, Shō Birational geometry and Manin's conjecture

ISBN:

9781009611640

100961164X

9781009611619

1009611615

OCLC:

1596676450

Publisher Number:

CIPO000392215

CIPO000404171

Access Restriction:

Restricted for use by site license