Holomorphic cotangent bundle
= Holomorphic cotangent bundle
{title2=$\Omega_X^1=(T^{1,0}X)^*$}
The dual of the <holomorphic tangent bundle> is a <holomorphic vector bundle> with local frames $dz^1,\ldots,dz^n$. Coordinate changes have holomorphic invertible Jacobian matrices, so these frames have holomorphic transition functions. Its <holomorphic sections> are exactly the <holomorphic one-forms>.