K-stability of Fano Varieties

Chenyang Xu

doi:10.1017/9781009538763

- Get access
  
  Buy a print copy
  
  Check if you have access via personal or institutional login
  
  Log in Register
Cited by 1
Cited by
- 1
Crossref Citations

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Miao, Minghao and Wang, Linsheng 2025. Kähler-Ricci solitons on Fano threefolds with non-trivial moduli. Mathematische Annalen,

CrossRef

Google Scholar

Chenyang Xu, Princeton University, New Jersey

Publisher:: Cambridge University Press
Online publication date:: May 2025
Print publication year:: 2025
Online ISBN:: 9781009538763
DOI:: https://doi.org/10.1017/9781009538763

Subjects:: Mathematics (general), Mathematics, Geometry and Topology
Series:: New Mathematical Monographs (50)

US$168.00

Digital access for individuals
(PDF download and/or read online)
Add to cart

Added to cart

Digital access for individuals
(PDF download and/or read online)
View cart
Export citation
Buy a print copy

Information

Contents

Metrics

Accessibility

The K-stability of Fano varieties has been a major area of research over the last decade, ever since the Yau-Tian-Donaldson conjecture was resolved. This is the first book to give a comprehensive algebraic treatment of this emerging field. It introduces all the notions of K-stability that have been used over the development of the subject, proves their equivalence, and discusses newly developed theory, including several new proofs for existing theorems. Aiming to be as self-contained as possible, the text begins with a chapter covering essential background knowledge, and includes exercises throughout to test understanding. Written by an author at the forefront of developments in the area, it will be a source of inspiration for graduate students and researchers who work in algebraic geometry.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge-org.demo.remotlog.com is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

References

Metrics

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

K-stability of Fano Varieties

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Notation and Conventions
pp ix-xii

Preliminaries
pp 1-11

1 - Higher Dimensional Geometry Background
pp 12-53

2 - K-stability via Test Configurations
pp 54-91

3 - K-stability via Filtrations
pp 92-137

4 - K-stability via Valuations
pp 138-206

5 - Higher Rank Finite Generation
pp 207-237

6 - Reduced Stability
pp 238-259

7 - K-moduliStack
pp 260-287

8 - K-moduli Space
pp 288-322

9 - Positivity of the CM Line Bundle
pp 323-364

Appendix A - Solutions to Exercises
pp 365-392

Glossary
pp 393-398

Bibliography
pp 399-408

Index
pp 409-411

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

K-stability of Fano Varieties

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown