Philipp Jell ; Johannes Rau ; Kristin Shaw - Lefschetz (1,1)-theorem in tropical geometry

epiga:4126 - Épijournal de Géométrie Algébrique, November 19, 2018, Volume 2 - https://doi.org/10.46298/epiga.2018.volume2.4126
Lefschetz (1,1)-theorem in tropical geometryArticle

Authors: Philipp Jell ; Johannes Rau ORCID; Kristin Shaw

    For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in the kernel of the eigenwave map. To prove this we establish a tropical version of the Lefschetz (1, 1)-theorem for rational polyhedral spaces that relates tropical line bundles to the kernel of the wave homomorphism on cohomology. Our result for tropical manifolds then follows by combining this with Poincaré duality for integral tropical homology.


    Volume: Volume 2
    Published on: November 19, 2018
    Accepted on: October 13, 2018
    Submitted on: December 5, 2017
    Keywords: Mathematics - Algebraic Geometry,14T05 (Primary), 52B40, 55N35, 14C25, 14C22 (Secondary)

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