Hyperbolic plane curves near the non-singular tropical limit

Cédric Le Texier (U. Toulouse)

08-Apr-2022, 14:00-15:00 (24 months ago)

Abstract: We determine necessary and sufficient conditions for real algebraic curves near the non-singular tropical limit to be hyperbolic with respect to a point, thus generalising Speyer's classification of stable curves near the tropical limit. In order to obtain the conditions, we develop tools of real tropical intersection theory. We introduce the tropical hyperbolicity locus and the signed tropical hyperbolicity locus of a real algebraic curve near the non-singular tropical limit, and show that it satisfies a real tropical analogue of convexity. In the case of honeycombs, we characterise the tropical hyperbolicity locus in terms of the set of twisted edges on the tropical limit.

algebraic geometrycombinatorics

Audience: researchers in the topic


(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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Organizers: Alicia Dickenstein*, Ethan Cotterill*, Cristhian Garay López*
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