Vol. 97, No. 2, 1981

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Torsion divisors on algebraic curves

George Kempf

Vol. 97 (1981), No. 2, 437–441
Abstract

Let D be a divisor on a smooth complete algebraic curve C such that the multiple dD is rationally equivalent to zero for some positive integer d. We may write D = D0 D where D0 and D are distinct effective divisors.

The purpose of this note is to prove the

Theorem. Assume that C is a curve with general moduli in characteristic zero. For such a divisor D, the cohomology H1(C,𝒪C(D0 + D)) must be zero (equivalently |K D0 D| is empty).

Mathematical Subject Classification 2000
Primary: 14H10
Secondary: 14C20
Milestones
Received: 30 January 1980
Published: 1 December 1981
Authors
George Kempf