MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Lefschetz (1,1)-theorem in Tropical Geometry

Kristin Shaw, Philipp Jell and Johannes Rau


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.

MSC Codes:
14T05, 52B40, 55N35, 14C25, 14C22

Related publications

2018 Journal Open Access
Philipp Jell, Johannes Rau and Kristin Shaw

Lefschetz (1,1)-theorem in tropical geometry

In: ÔEpijournal de géométrie algébrique, 2 (2018), p. 11