Kahler-einstein Metrics on Complex Surfaces With C(1) > 0

Tian, G.; Yau, Shing-Tung

doi:10.1007/BF01217685

Kahler-einstein Metrics on Complex Surfaces With C(1) > 0

G. Tian
(
- UC, San Diego
)
,
Shing-Tung Yau
(
- UC, San Diego
)

1987

29 pages

Published in:

Commun.Math.Phys. 112 (1987) 175-203

DOI:

10.1007/BF01217685

reference search51 citations

Citations per year

Abstract: (Springer)

Various estimates of the lower bound of the holomorphic invariant α(M), defined in [T], are given here by using branched coverings, potential estimates and Lelong numbers of positive,d-closed (1, 1) currents of certain type, etc. These estimates are then applied to produce Kähler-Einstein metrics on complex surfaces withC1>0, in particular, we prove that there are Kähler-Einstein structures withC1>0 on any manifold of differential type

CP^2 \# \overline {nCP^2 } (3 \leqq n \leqq 8)

.

FIELD THEORY: SPACE-TIME
MATHEMATICAL METHODS: TOPOLOGICAL
MATHEMATICAL METHODS: FIBRE BUNDLE

References(0)

Figures(0)

0 References