Abstract
We study the collection of homological equivalence relations on a fixed curve. We construct a moduli space for pairs consisting of a curve of genus g and a homological equivalence relation of degree n on the curve, and a classifying set for homological equivalence relations of degree n on a fixed curve, modulo automorphisms of the curve. We identify a special type of homological equivalence relations, and we characterize the special homological equivalence relations in terms of the existence of elliptic curves in the Jacobian of the curve.
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Guerra, L. Homological equivalence relations on an algebraic curve. Ann Univ Ferrara 64, 371–387 (2018). https://doi.org/10.1007/s11565-017-0295-x
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DOI: https://doi.org/10.1007/s11565-017-0295-x