In order to study the topology of real algebraic varieties, a combinatorial description of these spaces can be extremely useful. Such a description appears for example in “Viro's combinatorial patchworking” which is a powerful technique for studying the possible topological types of real algebraic hypersurfaces. I want to present a generalization of this description to higher codimensions which uses the idea of tropical limits. More precisely, given a family of real algebraic varieties with "non-singular tropical limit", we give a description of the topology a generic fiber via a "real structure" associated to the tropical limit. In my talk, I will explain tropical limits and how to use them to recover the topology.
(joint work with Kris Shaw and Arthur Renaudineau)