Linear systems on tropical curves

Christian Haase, Gregg Musiker, Josephine Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A tropical curve Γ is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical curve Γ analogously to the classical counterpart. We investigate the structure of |D| as a cell complex and show that linear systems are quotients of tropical modules, finitely generated by vertices of the cell complex. Using a finite set of generators, |D| defines a map from Γ to a tropical projective space, and the image can be modified to a tropical curve of degree equal to deg(D). The tropical convex hull of the image realizes the linear system |D| as a polyhedral complex.

Original languageEnglish (US)
Title of host publicationFPSAC'10 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics
Pages295-306
Number of pages12
StatePublished - Dec 1 2010
Event22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States
Duration: Aug 2 2010Aug 6 2010

Other

Other22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
CountryUnited States
CitySan Francisco, CA
Period8/2/108/6/10

Keywords

  • Canonical embedding
  • Chip-firing games
  • Divisors
  • Linear systems
  • Tropical convexity
  • Tropical curves

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