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Test Configurations, Stabilities and Canonical Kähler Metrics - Toshiki Mabuchi

Test Configurations, Stabilities and Canonical Kähler Metrics

Complex Geometry by the Energy Method

(Autor)

Buch | Softcover
128 Seiten
2021 | 1st ed. 2021
Springer Verlag, Singapore
978-981-16-0499-7 (ISBN)
CHF 97,35 inkl. MwSt
The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. 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.
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.

Introduction.- The Donaldson-Futaki invariant.- Canonical Kähler metrics.- Norms for test configurations.- Stabilities for polarized algebraic manifolds.- The Yau-Tian-Donaldson conjecture.- Stability theorem.- Existence problem.- Canonical Kähler metrics on Fano manifolds.- Geometry of pseudo-normed graded algebras.- Solutions.  

Erscheinungsdatum
Reihe/Serie SpringerBriefs in Mathematics
Zusatzinfo 37 Illustrations, black and white; X, 128 p. 37 illus.
Verlagsort Singapore
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 981-16-0499-1 / 9811604991
ISBN-13 978-981-16-0499-7 / 9789811604997
Zustand Neuware
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