The International Center for Mathematical Sciences – Sofia (ICMS-Sofia)


ICMS Seminar

8.11.2023, 16:00, Sofia time

ICMS-Sofia, Room 403

Tropicalizations II

Mikhail Shkolnikov, IMI-BAS

Abstract: I will start by briefly recalling the two approaches to tropicalizing subvarieties of algebraic tori. We then transition to the compactified version, substituting the torus with a toric variety, and formalizing the concept of embedded tropical varieties together with a notion of their smoothness. Notably, not all such varieties can be realized as tropicalizations of classical varieties, and different embeddings of classical varieties yield combinatorially distinct tropicalizations, which we equate through so-called modifications. We will conclude by addressing the question of recovering information about classical varieties from their tropicalizations, exemplified by the phase tropical limit having the same topology as corresponding complex hypersurfaces provided that the usual tropicalization is smooth.