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arXiv · 2004.00955

Complex and tropical counts via positive characteristic

Marco Pacini·Damiano Testa
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Abstract

We reconcile the discrepancy between the complex and tropical counts of some enumerative problems reducing to positive characteristic. Each problem that we consider suggests a prime with special behaviour. Modulo this prime, the solutions coalesce in uniform clusters: at this special prime, the geometric and the tropical behaviours match. As examples, we concentrate on inflection points of plane curves and theta-hyperplanes of canonical curves.

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Marco Pacini, Damiano Testa. 2020-04-02. Complex and tropical counts via positive characteristic. https://arxiv.org/abs/2004.00955

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