Abstract: In order to classify objects in singularity theory and algebraic geometry, we define invariants associated to varieties or germs of singularities and hope to have enough tools to compute them easily. From classical projective duality, for any variety X, we can define a dual variety X∗ and we call the class of X the degree of X∗. Plücker’s formula allows one to compute this class for plane curves with a certain set of nodes, cusps and tacnodes.

We will start our talk by recalling the general Bézout theorem and then present the Plücker-Teissier formula, which generalises Plücker’s formula to hypersurfaces, and we will sketch a method to generalise the approach to its proof to general complete intersections.