Lower bounds on the modified K-energy and complex deformations

Autor(es)

Clarke, Andrew ^[1] ; Tipler, Carl ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN MATHEMATICS; v. 252, p. 449-470, FEB 15 2014.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 11/07363-6 - Rigidez em espaços simétricos
• Beneficiário: Andrew James Clarke
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado