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Tropical lifting problem for the intersection of plane curves

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Abstract

Given a tropical divisor D in the intersection of two tropical plane curves, we study when it can be realized as the tropicalization of the intersection of two algebraic curves, and give a sufficient condition. It is shown that under a certain condition involving a graph determined by these tropical curves, we can algorithmically find algebraic curves such that the tropicalization of their intersection is D.

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Acknowledgements

I am grateful to Nobuyoshi Takahashi for helpful comments. This work was supported by JST, the establishment of university fellowships towards the creation of science technology innovation, Grant Number JPMJFS2129.

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  1. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan

    Masayuki Sukenaga

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  1. Masayuki Sukenaga
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Correspondence to Masayuki Sukenaga.

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Sukenaga, M. Tropical lifting problem for the intersection of plane curves. Beitr Algebra Geom (2023). https://doi.org/10.1007/s13366-023-00705-y

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