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SpringerBriefs in Mathematics

Test Configurations, Stabilities and Canonical Kähler Metrics

Complex Geometry by the Energy Method

Authors: Mabuchi, Toshiki

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  • The main theme of our book is the very hot issue known as the Yau-Tian-Donaldson conjectureAs to the Yau-Tian-Donaldson conjecture, we focus on the open case on the existence of extremal Kähler metrics
  • In our approach to the existence problem of extremal metrics, we use the Chow norm very effectively
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eBook 46,00 €
price for Spain (gross)
  • ISBN 978-981-16-0500-0
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Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-981-16-0499-7
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  • Covid-19 shipping restrictions
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About this book

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed.

It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds.

Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding’s functional, and plays a crucial role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-981-16-0500-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-981-16-0499-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Test Configurations, Stabilities and Canonical Kähler Metrics
Book Subtitle
Complex Geometry by the Energy Method
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2021
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-16-0500-0
DOI
10.1007/978-981-16-0500-0
Softcover ISBN
978-981-16-0499-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 128
Number of Illustrations
37 b/w illustrations
Topics