The Degree of the Tangent and Secant Variety to a Projective Surface

Abstract

In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample. This method exploits the link between these varieties and the Hilbert scheme $0$-dimensional subschemes of length $2$ of the surface.