ABSTRACT
Let π:C → B be a (possibly ramified) covering map between smooth curves over an algebraically closed field with the genus of B being at least two. A question due to David Prill asks whether h 0(X, 𝒪 C (π−1(b))) = 1 for the general closed point b ∈ B. We investigate this question. If C is hyperelliptic, then h 0(X, 𝒪 C (π−1(b))) = 1 for the general closed point b ∈ B.
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#Communicated by L. Ein.