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Jul 25, 2017 at 3:29 comment added user21574 For hyperkahler manifold, S.Boucksom showed that a $(1, 1)$ class $ \{\omega\} $ is Kahler if and only if it lies in the positive part of the Beauville-Bogomolov quadratic cone and moreover $\int_C \omega > 0$ for all rational curves $C ⊂ X$. For general case it is a conjecture yet! SEE : Cones positifs des varietes complexes compactes, Thesis, Grenoble 2002.
Jul 2, 2014 at 18:39 vote accept Italo
Jul 2, 2014 at 13:19 answer added Robert Bryant timeline score: 10
Jul 2, 2014 at 12:37 history asked Italo CC BY-SA 3.0