Complex and tropical counts via positive characteristic

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2022-12-01 DOI:10.1016/j.exmath.2022.07.003

Marco Pacini , Damiano Testa

引用次数: 2

Abstract

We study two classical families of enumerative problems: inflection lines of plane curves and theta-hyperplanes of canonical curves. In these problems the complex counts and the tropical counts disagree. Each problem suggests a prime with special behavior. On the one hand, we analyze the reduction modulo these special primes, and we prove that the complex solutions coalesce in uniform clusters. On the other hand, we observe that the counts in special characteristic and in tropical geometry match.

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复杂和热带计数通过阳性特征

研究了两类经典的枚举问题:平面曲线的拐点线和正则曲线的超平面。在这些问题中，复杂计数和热带计数不一致。每个问题都提出一个具有特殊行为的素数。一方面，我们分析了这些特殊素数的约简模，并证明了复解在一致簇中聚并。另一方面，我们观察到，在特殊的特征和热带几何匹配计数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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