Mabuchi Test Configurations, Stabilities and Canonical Kähler Metrics
1. Auflage 2021
ISBN: 978-981-16-0500-0
Verlag: Springer Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark
Complex Geometry by the Energy Method
E-Book, Englisch, 128 Seiten
Reihe: SpringerBriefs in Mathematics
ISBN: 978-981-16-0500-0
Verlag: Springer Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.Zielgruppe
Graduate
Autoren/Hrsg.
Weitere Infos & Material
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.