Plücker formulae for curves in high dimensions

Abstract

The classical relations of Plücker between the invariants and singularities of a plane curve can be expressed as two linear relations and two involving quadratic terms. The linear relations were generalised to curves in n-space already in the nineteenth century, but true generalisations of the others were obtained only in 3-space. In this article, using the classical method of correspondences, we obtain formulae in n-space corresponding to the original ones in the plane.