Terminology for Holomorphic and Anti-Holomorphic Forms - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T19:57:33Z http://mathoverflow.net/feeds/question/49687 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/49687/terminology-for-holomorphic-and-anti-holomorphic-forms Terminology for Holomorphic and Anti-Holomorphic Forms Dyke Acland 2010-12-16T22:30:11Z 2010-12-17T02:14:10Z <p>For any complex manifold \$M\$ we have the usual decomposition of the cotangent bundle into the direct sum \$\Omega^{(1,0)} \oplus \Omega^{(0,1)}\$. I know these two sub-modules as the holomorphic and anti-holomorphic forms respectively. However, I have been told that this is the terminology usually used by physicists. How to mathematicians refer to \$\Omega^{(1,0)}\$ and \$\Omega^{(0,1)}\$?</p>