Note on curves in a Jacobian
Abstract
For a curve C, viewed as a cycle in its Jacobian, we study its image n*C under multiplication by n on JC. We prove that the subgroup generated by these cycles, in the Chow group modulo algebraic equivalence, has rank at most d-1, where d is the gonality of C. We also discuss some general facts on the action of n* on the Chow groups.
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