In particular, do Fano Kahler surfaces with reverse orientation admit Kahler-Einstein metrics?
$\begingroup$
$\endgroup$
1
-
4$\begingroup$ By a result of Kotschick, a compact complex surface which admits a complex structure for the reverse orientation has signature $0$. For Fano (= Del Pezzo) surfaces, this happens only for $\mathbb{P}^1\times \mathbb{P}^1$, in which case you can conclude by yourself. $\endgroup$– abxApr 13, 2016 at 18:09
Add a comment
|