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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Lower bounds on the modified K-energy and complex deformations

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Author(s):
Clarke, Andrew [1] ; Tipler, Carl [2]
Total Authors: 2
Affiliation:
[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ - Brazil
[2] Univ Quebec, Dept Math, Succursale Ctr Ville, Montreal, PQ H3C 3P8 - Canada
Total Affiliations: 2
Document type: Journal article
Source: ADVANCES IN MATHEMATICS; v. 252, p. 449-470, FEB 15 2014.
Web of Science Citations: 0
Abstract

Let (X, L) be a polarized Kahler manifold that admits an extremal metric in c(1) (L). We show that on a nearby polarized deformation (X', L') that preserves the symmetry induced by the extremal vector field of (X, L), the modified K-energy is bounded from below. This generalizes a result of Chen, Szekelyhidi and Tosatti {[}8,35,38] to external metrics. Our proof also extends a convexity inequality on the space of Kahler potentials due to X.X. Chen {[}7] to the extremal metric setup. As an application, we compute explicit polarized 4-points blow-ups of CP1 x CP1 that carry no extremal metric but with modified K-energy bounded from below. (C) 2013 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 11/07363-6 - Rigidity in symmetric spaces
Grantee:Andrew James Clarke
Support Opportunities: Scholarships in Brazil - Post-Doctoral