An analogue of Abel's theorem

2002/11/18 by Herbert Clemens, Clemens, Herbert
Mathematics · #14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C25

paper · pdf · doi:10.48550/arxiv.math/0211282

18 pages, latex2e file

arxiv created 2002/11/18 · arxiv updated 2009/11/30

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.

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