An Analogue of Abel’s Theorem

Herbert Clemens

A chapter in The Legacy of Niels Henrik Abel, 2004, pp 511-530 from Springer

Abstract: Abstract This work makes a parallel construction for curves on threefolds to a “current-theoretic” proof of Abel’s theorem giving the rational equivalence of divisors P and Q on a Riemann surface when Q - P is (equivalent to) zero in the Jacobian variety of the Riemann surface. The parallel construction is made for homologous “sub-canonical” curves P and Q on a general class of threefolds. If P and Q are algebraically equivalent and Q - P is zero in the (intermediate) Jacobian of a threefold, the construction “almost” gives rational equivalence.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18908-1_14

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DOI: 10.1007/978-3-642-18908-1_14

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