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On the multiplicative structure of sections of vector bundles on an algebraic curve

Abstract Here we study (in a more general setting) the following problem. Let C be a smooth projective curve, E and F vector bundles on C and V ⊆ H0 (C, E) (resp. W ⊆ H0 (C, F)) vector spaces generically spanning E (resp. F); find lower bounds for the dimension of the image of the multiplication map V ⊗ W → H0 (C, E ⊗ F) generalizing the case rank(E) = rank(F) = 1.