Effective base point freeness on moduli spaces of
        vector bundles on curves

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We will present a few results on effective bounds for the
global generation of multiples of generalized theta line bundles
on moduli spaces of vector bundles on a curve X. The techniques
involved are of two different flavors: on one hand we will use
a result (of independent interest) giving an optimal upper bound
on the dimension of the Hilbert scheme of coherent quotients
of a fixed vector bundle, while on the other hand we will appeal
to general vector bundle techniques on abelian varieties via the
notion of Verlinde bundle on the Jacobian of X. If time allows we
will briefly address problems related to normal generation and
base points for these linear series.