Compact hyperkähler manifolds: Basic results. (English) Zbl 0953.53031

Huybrechts, Daniel

Invent. Math. 135, No. 1, 63-113 (1999).

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”.

Reviewer: D.-Q.Zhang (Singapore)

MSC:

53C26	Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
14J28	\(K3\) surfaces and Enriques surfaces

Keywords:

hyper-Kähler manifold; Torelli theorem; Kähler cone