Riemann-Roch theory for weighted graphs and tropical curves

Omid Amini; Lucia Caporaso

doi:10.1016/j.aim.2013.03.003

Riemann-Roch theory for weighted graphs and tropical curves

Omid Amini
, Lucia Caporaso

University Roma Tre

Research output: Contribution to journal › Article › peer-review

Abstract

We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann-Roch theorem holds in both cases. We extend Baker's Specialization Lemma to weighted graphs.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Advances in Mathematics
Volume	240
DOIs	https://doi.org/10.1016/j.aim.2013.03.003
Publication status	Published - 1 Jun 2013

Keywords

Algebraic curve
Divisor
Graph
Riemann-Roch
Tropical curve
Weighted graph

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10.1016/j.aim.2013.03.003

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title = "Riemann-Roch theory for weighted graphs and tropical curves",

abstract = "We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann-Roch theorem holds in both cases. We extend Baker's Specialization Lemma to weighted graphs.",

keywords = "Algebraic curve, Divisor, Graph, Riemann-Roch, Tropical curve, Weighted graph",

author = "Omid Amini and Lucia Caporaso",

year = "2013",

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AU - Caporaso, Lucia

PY - 2013/6/1

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N2 - We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann-Roch theorem holds in both cases. We extend Baker's Specialization Lemma to weighted graphs.

AB - We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann-Roch theorem holds in both cases. We extend Baker's Specialization Lemma to weighted graphs.

KW - Algebraic curve

KW - Divisor

KW - Graph

KW - Riemann-Roch

KW - Tropical curve

KW - Weighted graph

UR - https://www.scopus.com/pages/publications/84875673485

U2 - 10.1016/j.aim.2013.03.003

DO - 10.1016/j.aim.2013.03.003

M3 - Article

AN - SCOPUS:84875673485

SN - 0001-8708

VL - 240

SP - 1

EP - 23

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Riemann-Roch theory for weighted graphs and tropical curves

Abstract

Keywords

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