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Tropical rational curves with first order tangency via WDVV

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arxiv 2501.16927 v1 pith:4E77ZXI7 submitted 2025-01-28 math.AG

Tropical rational curves with first order tangency via WDVV

classification math.AG
keywords tropicalcurvesrationaltangencydegreefirstorderplane
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In this article, we study the tropical counterpart of the enumeration of rational curves in $\mathbb{CP}^2$ with first order tangency. We use the tropical analogue of the WDVV technique to compute rational tropical plane curves of degree $d$ tangent to a degree $l$ tropical plane curve and passing through $3d-2$ points in general position. As Mikhalkin's correspondence suggests, our numbers agree with earlier results on tangency in complex geometry.

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