We give an upper bound on the dimension of the Hilbert scheme of quotients of an arbitrary vector bundle on a smooth projective curve, depending on the minimal degree of such a quotient. The bound is used for deriving effective base point freeness statements for generalized theta linear series on moduli spaces of vector bundles.
"Dimension estimates for Hilbert schemes and effective base point freeness on moduli spaces of vector bundles on curves." Duke Math. J. 107 (3) 469 - 495, 15 April 2001. https://doi.org/10.1215/S0012-7094-01-10732-1