  We prove a topological result concerning the kernel of a morphism d : E --> F
of holomorphic vector bundles over a complex analytic space. As a consequence,
we show that the projectivization P(ker d) is a quasifibration up to some
dimension. We give an application to the Abel-Jacobi map of a Riemann surface,
and to the space of rational curves in the symmetric product of a Riemann
surface.
