Abstract
We prove a topological result concerning the kernel ker d 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.
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