Holomorphic conormal bundle
= Holomorphic conormal bundle
{title2=$N^*_{Y/X}$}
For a <complex submanifold> $Y\subset X$, the holomorphic conormal bundle is the annihilator of $T^{1,0}Y$ inside $\Omega_X^1|_Y$, or equivalently the dual of the <holomorphic normal bundle>. For a smooth analytic hypersurface with local equation $f$, it is generated by $df|_Y$. It is also the locally free analytic sheaf $\mathcal I_Y/\mathcal I_Y^2$.