Diffeomorphically vs holomorphically trivial canonical bundle - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-19T03:08:46Z http://mathoverflow.net/feeds/question/16327 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16327/diffeomorphically-vs-holomorphically-trivial-canonical-bundle Diffeomorphically vs holomorphically trivial canonical bundle Stergios 2010-02-25T00:01:13Z 2010-02-25T00:01:13Z <blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/15003/two-definitions-of-calabi-yau-manifolds" rel="nofollow">Two definitions of Calabi-Yau manifolds</a> </p> </blockquote> <p>Given a compact kahler manifold M with diffeomorphically trivial canonical bundle. Is it true that the canonical bundle is also holomorphically trivial ?</p> <p>What if M is only assumed to be a compact complex manifold ?</p>