A generalization of Abel's Theorem and the Abel--Jacobi map

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dc.creatorDupont, Johan L.
dc.creatorKamber, Franz W.
dc.date2008-11-06
dc.date2008-12-02
dc.date.accessioned2026-07-07T12:08:03Z
dc.date.available2026-07-07T12:08:03Z
dc.descriptionWe generalize Abel's classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold $M^d \subset X^n$ in a compact oriented Riemannian $n$--manifold, or more generally for any $d$--cycle $Z$ relative to a triangulation of $X$, we define a (simplicial) $(n-d-1)$--gerbe $Λ_{Z}$, the Abel gerbe determined by $Z$, whose vanishing as a Deligne cohomology class generalizes the notion of `linear equivalence to zero'. In this setting, Abel's theorem remains valid. Moreover we generalize the classical Inversion Theorem for the Abel--Jacobi map, thereby proving that the moduli space of Abel gerbes is isomorphic to the harmonic Deligne cohomology; that is, gerbes with harmonic curvature.
dc.description27 pages Added references; minor changes in text; corrected typos
dc.identifierhttps://arxiv.org/abs/0811.0961
dc.identifierhttp://arxiv.org/abs/0811.0961
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209184
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject55R20, 57R30
dc.titleA generalization of Abel's Theorem and the Abel--Jacobi map
dc.typetext

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