Abstract: | Let ℒ︁ be a line bundle on a smooth curve C of genus g ≥ 2 and let W ⊂ H0 (ℒ︁) be a subspace of dimension r +1, in this paper we study the natural map μW : W ⊗ H0 (ωC) → H0 (ℒ︁ ⊗ ωC). Let D ⊂ G(r + 1, H0(ℒ︁)) be the locus where μW fails to be surjective: we prove that, if C is not hyperelliptic of genus g ≥ 3, D is an irreducible and reduced divisor on G(r + 1, H0(ℒ︁)) for any r ≥ 3, and for r = 2 if the curve C is not trigonal. |