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Compact hyperkähler manifolds: Basic results. (English) Zbl 0953.53031
We quote some paragraph from a succeeding paper [named [2], the author, “The Kähler cone of a compact hyper-Kähler manifold” (http://front.math.ucdavis.edu/math.AG/9909109)]: “As was pointed out by D. Kaledin, the proof of the projectivity criterion in the paper under review [named[1]]contains a serious mistake (from dimension four on). Almost all the results formulated here (in paper [2]) and many of those in the paper are, for the moment, not fully proved”.

##### MSC:
 53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 14J28 $$K3$$ surfaces and Enriques surfaces
##### Keywords:
hyper-Kähler manifold; Torelli theorem; Kähler cone
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