Lifting tropical self intersections

Yoav Len; Matt  Satriano

doi:10.1016/j.jcta.2019.105138

Lifting tropical self intersections

Yoav Len, Matt Satriano

Pure Mathematics

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

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.

Original language	English
Article number	105138
Number of pages	21
Journal	Journal of Combinatorial Theory, Series A
Volume	170
Early online date	4 Oct 2019
DOIs	https://doi.org/10.1016/j.jcta.2019.105138
Publication status	Published - Feb 2020

Keywords

Tropical geometry
Intersection theory
Divisor theory
Chip-firing
Polyhedral complexes
Elliptic curves

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10.1016/j.jcta.2019.105138

Lifting tropical self intersections
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
Accepted author manuscript, 358 KBLicence: CC BY-NC-ND

Cite this

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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.",

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AB - 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.

KW - Tropical geometry

KW - Intersection theory

KW - Divisor theory

KW - Chip-firing

KW - Polyhedral complexes

KW - Elliptic curves

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DO - 10.1016/j.jcta.2019.105138

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VL - 170

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

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Lifting tropical self intersections

Abstract

Keywords

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