Multiplication of sections and Clifford bounds for stable vector bundles on curves

A sharp lower bound for the rank of the natural multiplication map H-0(F)xH(0)(G) --> H-0(FxG) is given, F and G being vector bundles generically generated by their global sections on an integral projective variety. Some Clifford-type inequalities in the context of the Brill-Noether theory of vector bundles on a curve are proved and their sharpness is studied.