Work

Realizability of tropical pluri‐canonical divisors

Year: 2024

Type: article

Abstract: Consider a pair consisting of an abstract tropical curve and an effective divisor from the linear system associated to times the canonical divisor for . In this article, we give a purely combinatorial criterion to determine if such a pair arises as the tropicalization of a pair consisting of a smooth algebraic curve over a non‐Archimedean field with algebraically closed residue field of characteristic 0 together with an effective pluri‐canonical divisor. To do so, we introduce tropical normalized covers as special instances of cyclic tropical Hurwitz covers and reduce the realizability problem for pluri‐canonical divisors to the realizability problem for normalized covers. Our main result generalizes the work of Möller–Ulirsch–Werner on realizability of tropical canonical divisors and incorporates the recent progress on compactifications of strata of ‐differentials in the work of Bainbridge–Chen–Gendron–Grushevsky–Möller.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70027

Authors: Felix Röhrle, Johannes Schwab

Institutions: University of Tübingen, Goethe University Frankfurt

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funder: Deutsche Forschungsgemeinschaft