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

epiga:4126 - Épijournal de Géométrie Algébrique, 19 novembre 2018, Volume 2
Lefschetz (1,1)-theorem in tropical geometry

Auteurs : Jell, Philipp and Rau, Johannes and Shaw, Kristin

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 Poincar\'e duality for integral tropical homology.


Source : oai:arXiv.org:1711.07900
Volume : Volume 2
Publié le : 19 novembre 2018
Déposé le : 5 décembre 2017
Mots-clés : Mathematics - Algebraic Geometry,14T05 (Primary), 52B40, 55N35, 14C25, 14C22 (Secondary)


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