Real phase structures on tropical varieties

Abstract: In this talk, I will propose a definition of real phase structures on tropical varieties. I’ll explain that when the tropical variety is a matroid fan, specifying a real phase structure is cryptomorphic to providing an orientation of the underlying matroid.

I’ll define the real part of a tropical variety with a real phase structure. This determines a closed chain in an appropriate homology theory. In the case when the tropical variety is non-singular, the real part is a PL-manifold. Moreover, for tropical manifolds equipped with real phase structures we can apply the same spectral sequence for hypersurfaces, obtained by Renaudineau and myself, and bound the Betti numbers of the real part by the dimensions of the tropical homology groups.

This is joint work in progress with Johannes Rau and Arthur Renaudineau.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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