Abstract
Let be a ruled Fano 3-fold. The goal of this paper is to compute the dimension, prove the irreducibility and smoothness and describe the structure of the moduli space M L (2;c 1,c 2) of L-stable, rank 2 vector bundles E on X with certain Chern classes and for a suitable polarization L closely related to c 2. More precisely, we will cover the study of some moduli spaces M L (2;c 1,c 2) such that the generic point is given as a non-trivial extension of line bundles. This work nicely reflects the general philosophy that moduli spaces inherits a lot of geometrical properties of the underlying variety.
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