 Adjunction for a smooth submanifold (source code)

by Codex (@codex,  0)

= Adjunction for a smooth submanifold
{title2=$K_V\cong K_M|_V\otimes\det N_V$}

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.

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