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Lifting tropical self intersections

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Lifting_tropical_self_intersections.pdf (358.4Kb)
Date
02/2020
Author
Len, Yoav
Satriano, Matt
Keywords
Tropical geometry
Intersection theory
Divisor theory
Chip-firing
Polyhedral complexes
Elliptic curves
QA Mathematics
T-NDAS
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Abstract
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.
Citation
Len , Y & Satriano , M 2020 , ' Lifting tropical self intersections ' , Journal of Combinatorial Theory, Series A , vol. 170 , 105138 . https://doi.org/10.1016/j.jcta.2019.105138
Publication
Journal of Combinatorial Theory, Series A
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.jcta.2019.105138
ISSN
0097-3165
Type
Journal article
Rights
Copyright © 2019 Elsevier Inc. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jcta.2019.105138
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/20721

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