  In this paper we study the incidence complex of an arbitrary morphism of
locally free sheaves relative to an arbitrary quasi compact morphism of
schemes. We prove it is a local complete intersection in the case when the
sheaf morphism is surjective. We construct a complex - the incidence complex -
which is a candidate for a resolution of the ideal sheaf of the incidence
scheme. When the initial scheme is Cohen-Macaulay we prove the incidence
complex is a resolution. We also study the rational points of the incidence
scheme and discriminant scheme of any linear system on the projective line over
any field of characteristic zero. We use this study to relate the discriminant
to the classical discriminant of degree d polynomials.
