Polynomial properties of tropical refined invariants

Abstract: Tropical geometry is a useful tool in the enumeration of complex or real algebraic curves. Around 10 years ago Block and Göttsche proposed a kind of quantification of tropical enumerative invariants, which are Laurent polynomial interpolating between complex and real enumerative invariants. In this talk I will review these tropical refined invariants and their relation with classical enumerative geometry. I will then explain some curious polynomial behavior of the coefficients of these refined invariants, providing in particular a surprising resurgence, in a dual setting, of the so-called node polynomials and Göttsche conjecture.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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