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Lifting tropical self intersections

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Lifting tropical self intersections. / Len, Yoav; Satriano, Matt .

In: Journal of Combinatorial Theory, Series A, Vol. 170, 105138, 02.2020.

Research output: Contribution to journalArticlepeer-review

Harvard

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

APA

Len, Y., & Satriano, M. (2020). Lifting tropical self intersections. Journal of Combinatorial Theory, Series A, 170, [105138]. https://doi.org/10.1016/j.jcta.2019.105138

Vancouver

Len Y, Satriano M. Lifting tropical self intersections. Journal of Combinatorial Theory, Series A. 2020 Feb;170. 105138. https://doi.org/10.1016/j.jcta.2019.105138

Author

Len, Yoav ; Satriano, Matt . / Lifting tropical self intersections. In: Journal of Combinatorial Theory, Series A. 2020 ; Vol. 170.

Bibtex - Download

@article{089b348b477a46e79c84bf0a5b7f1a57,
title = "Lifting tropical self intersections",
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.",
keywords = "Tropical geometry, Intersection theory, Divisor theory, Chip-firing, Polyhedral complexes, Elliptic curves",
author = "Yoav Len and Matt Satriano",
year = "2020",
month = feb,
doi = "10.1016/j.jcta.2019.105138",
language = "English",
volume = "170",
journal = "Journal of Combinatorial Theory, Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Lifting tropical self intersections

AU - Len, Yoav

AU - Satriano, Matt

PY - 2020/2

Y1 - 2020/2

N2 - 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.

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

U2 - 10.1016/j.jcta.2019.105138

DO - 10.1016/j.jcta.2019.105138

M3 - Article

VL - 170

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

SN - 0097-3165

M1 - 105138

ER -

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