Lifting tropical self intersections

We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral complex and compute its dimension. When the genus is at most 1, w...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 170; p. 105138
Main Authors Len, Yoav, Satriano, Matthew
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2020
Subjects
Chip-firing
Divisor theory
Elliptic curves
Intersection theory
Polyhedral complexes
Tropical geometry
Tropical geometry
Polyhedral complexes
Intersection theory
Elliptic curves
Chip-firing
Divisor theory
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ISSN0097-3165
1096-0899
DOI10.1016/j.jcta.2019.105138

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Summary:We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral complex and compute its dimension. When the genus is at most 1, we show that all the tropical divisors that move in the expected dimension are realizable. As part of the proof, we introduce a combinatorial tool for explicitly constructing large families of realizable tropical divisors.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2019.105138