Pacini, Marco and Testa, Damiano (2022) Complex and tropical counts via positive characteristic. Expositiones Mathematicae, 40 (4). pp. 1096-1115. doi:10.1016/j.exmath.2022.07.003 ISSN 0723-0869.

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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.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Expositiones Mathematicae
Publisher:	Elsevier
ISSN:	0723-0869
Official Date:	December 2022
Dates:	Date Event December 2022 Published 4 November 2022 Available 6 July 2022 Accepted
Volume:	40
Number:	4
Page Range:	pp. 1096-1115
DOI:	10.1016/j.exmath.2022.07.003
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	4 August 2022
Related URLs:	Publisher

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