EINSTEIN-KAHLER METRIC ON MANIFOLDS WITH POSITIVE FIRST CHERN CLASS

Authors
REAL C
Citation
C. Real, EINSTEIN-KAHLER METRIC ON MANIFOLDS WITH POSITIVE FIRST CHERN CLASS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 322(5), 1996, pp. 461-464
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
322
Issue
5
Year of publication
1996
Pages
461 - 464
Database
ISI
SICI code
0764-4442(1996)322:5<461:EMOMWP>2.0.ZU;2-L
Abstract
To prove the existence of an Einstein-Kahler metric on compact Kahler manifolds with positive first Chern class, we study the invariant alph a(Gp), introduced by Tan, first on P-m (C) then on the hypersurface of Fermat X(m,p). We prove the conjecture of Tan and Yau: alpha(Gp) (P-m (C)) greater than or equal to inf{1, p/(m + 1)}. This yields the theo rem: if p greater than or equal to (m + 2)/2, there is on X(m,p) an Ei nstein-Kahler metric.