| Résume | In our talk we will present an adjunction type formula. Given a projective variety $X$ we assume it to be Cohen-Macaulay, so that it has a dualizing sheaf $\omega_X$. Once we chose a complete intersection $Z\subset \mathbb P^n_k$ that contains $X$ as a closed subvariety we have $((0:I_X)\omega_Z)_{|X}=\omega_X$, where $I_X$ is the ideal sheaf defining $X$ inside $Z$. We establish a couple of applications. Chief among them we prove a multiplicity formula for the Milnor number of a Gorenstein curve, with the help of the local version of our adjunction formula. This formula has been previously established for complete intersections and smoothable curves. This is a joint work with Antoni Rangachev.
|
