CAMEGEST
Extremal Kaehler metrics and geometric stability
| Coordinatore | UNIVERSITA DEGLI STUDI DI PARMA
Organization address
address: VIA UNIVERSITA 12 contact info |
| Nazionalità Coordinatore | Italy [IT] |
| Totale costo | 228˙804 € |
| EC contributo | 228˙804 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2009-IOF |
| Funding Scheme | MC-IOF |
| Anno di inizio | 2010 |
| Periodo (anno-mese-giorno) | 2010-09-15 - 2013-09-14 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITA DEGLI STUDI DI PARMA
Organization address
address: VIA UNIVERSITA 12 contact info |
IT (PARMA) | coordinator | 228˙804.70 |
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Obiettivo del progetto (Objective)
'The problem of finding canonical Kaehler metrics on compact manifolds is central in Kaehler geometry. Since the pioneering work of Calabi, the existence problem for Kaehler-Einstein (and more generally constant scalar curvature, or even extremal Kaehler) metrics has attracted considerable attention. In this circle of ideas the most fascinating problem is represented by the so-called Yau-Tian-Donaldson conjecture, which predict the equivalence between the K-polystability of a polarized manifold and the existence of a constant scalar curvature (or more generally extremal) Kaehler metric in the polarization class. In this vein we propose the following three main research objectives: first, find an algebraic criterion for K-stability of polarized manifolds; second, study the effect of symplectic reduction on relative K-stability; third study the Calabi flow (in particular on toric manifolds) adapting the La Nave-Tian and Arezzo-La Nave approach to the Kahhler-Ricci flow. We propose to develop the research at Princeton University, under the superfision of prof. G. Tian, and Parma University, under the supervision of prof. C. Arezzo.'