Computing Linear Systems on Metric Graphs

Abstract

The linear system of a divisor $D$ on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it – they serve as the landmarks for us to compute the $f$-vector of the complex and find all cells in the complex. A linear system can also be identified as a tropical convex hull of rational functions. We compute its extremal generators using the landmarks. We apply these methods to some examples – namely the canonical linear systems of some small trivalent graphs.

Publication
Journal of Symbolic Computation, 2018, 87(3), 54-67
Bo Lin
Bo Lin
Visiting Assistant Professor

My research interests include mathematical biology, tropical geometry and combinatorics.

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