English

An analogue of Abel's theorem

Algebraic Geometry 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0211282,
  title  = {An analogue of Abel's theorem},
  author = {Herbert Clemens},
  journal= {arXiv preprint arXiv:math/0211282},
  year   = {2007}
}

Comments

18 pages, latex2e file

R2 v1 2026-07-22T16:49:30.764Z