Adjunction for a smooth submanifold ($K_V\cong K_M{|}_V\otimes \det N_V$)

For a smooth complex submanifold $V\subset M$, the tangent exact sequence gives $\det TM{|}_V=\det TV\otimes \det N_V$. Dualizing yields $K_V=K_M{|}_V\otimes \det N_V$. This form of Adjunction formula applies in any codimension.