Buchdahl, N.2006-06-192006-06-192003Annals of Global Analysis and Geometry, 2003; 23(2):189-2040232-704X1572-9060http://hdl.handle.net/2440/3452The original publication can be found at www.springerlink.comThe classical conjectures of Weil on K3 surfaces – that the set of such surfaces is connected; that a version of the Torelli theorem holds; that each such surface is Kähler; and that the period map is surjective – are reconsidered in the light of a generalisation of the Nakai-Moishezon criterion, and short proofs of all the conjectures are given. Most of the proofs apply equally or with minor variation to complex 2-tori, the only other compact Kähler surfaces with trivial canonical bundle.en© 2003 Kluwer Academic PublishersKähler surfaceK3 surfacecomplex 2-torusperiod mapTorelli theoremJournal article002003080510.1023/A:10225570046240001810436000062-s2.0-003728225358581Buchdahl, N. [0000-0003-3520-6618]