Work

Lefschetz (1,1)-theorem in tropical geometry

Year: 2018

Type: article

Abstract: 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. Comment: 27 pages, 6 figures, POSTpublished version with minor corrections and improvements; the published version is arxiv.org/abs/1711.07900v3

Source: Épijournal de Géométrie Algébrique

DOI: 10.46298/epiga.2018.volume2.4126

Authors: Philipp Jell, Johannes Rau, Kristin Shaw

Institutions: Georgia Institute of Technology, University of Oslo, University of Tübingen

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Université de Genève, Bergens Forskningsstiftelse

Awards: G5741529951, G6467214320