Rationality of Varieties

This book provides an overview of the latest progress on rationality questions in algebraic geometry, covering topics such as universal triviality of the Chow group, stable birationality, cubic and Fano fourfolds, rationality of moduli spaces, and birational invariants of group actions. It originated from conferences on the islands Texel and Schiermonnikoog and is a continuation of the tradition of earlier volumes in the series.

Format: Hardback
Length: 433 pages
Publication date: 20 October 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book offers a thorough exploration of the latest advancements in rationality questions within the realm of algebraic geometry. It delves into diverse topics such as the universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces, and birational invariants of group actions on varieties. These groundbreaking developments have been contributed by esteemed experts in their respective fields, making this volume a valuable resource for scholars and researchers in the field.

The study of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a rich history and has played a crucial role in the development of algebraic geometry. In recent years, significant progress has been made in this area, leading to a renewed interest in this question. This resurgence has been fueled by the organization of a series of conferences on the island of Schiermonnikoog, with the latest volume in the series being dedicated to exploring these recent developments.

The book follows in the footsteps. tradition of earlier volumes, which originated from conferences held on the islands of Texel and Schiermonnikoog. This series of conferences has become a prominent platform for researchers to exchange ideas and share their latest findings in the field. The book serves as a valuable resource for those seeking to stay updated on the latest advancements in rationality questions in algebraic geometry.

The chapters in this book are written by leading experts in their respective fields, providing in-depth insights and perspectives on the topics discussed. Each chapter is accompanied by detailed examples and exercises to aid in understanding and applying the concepts presented. The book also includes a comprehensive bibliography that provides further reading for those interested in exploring these topics in greater detail.

In conclusion, this book provides a comprehensive overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces, and birational invariants of group actions on varieties. The contributions of the esteemed experts in their respective fields make this volume a valuable resource for scholars and researchers in the field. Whether you are a seasoned researcher or just starting in algebraic geometry, this book will provide you with the necessary knowledge and insights to advance your understanding of these complex topics.

Weight: 828g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030754204
Edition number: 1st ed. 2021