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arXiv · 2209.15478

Tropical Linear Series and Tropical Independence

David Jensen·Sam Payne
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Abstract

We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine notion of rank with the notion of tropical independence and has the property that the restriction of a tropical linear series of rank r to a connected subgraph is a tropical linear series of rank r. We show that tropical linear series of rank 1 are finitely generated as tropical modules and state a number of open problems related to algebraic, combinatorial, and topological properties of higher rank tropical linear series

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David Jensen, Sam Payne. 2022-09-30. Tropical Linear Series and Tropical Independence. https://arxiv.org/abs/2209.15478

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