18 citations · 25 across the 6 of their papers we have counts for
6 papers
Continuity of the superpotentials and slices of tropical currents
Farhad Babaee, Tien Cuong Dinh
We study the question of the continuity of slices of currents and explain how it relates to several seemingly unrelated problems in tropical geometry. On the one hand, through this…
Extremal decompositions of tropical varieties and relations with rigidity theory
Farhad Babaee, Sean Dewar, James Maxwell
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard…
Dynamical Tropicalisation
Farhad Babaee
We analyse the dynamics of the pullback of the map on the complex tori and toric varieties. We will observe that tropical objects naturally appear in the limit,…
Convexity of complements of tropical varieties, and approximations of currents
Karim Adiprasito, Farhad Babaee
The goal of this note is to affirm a local version of the conjecture of Nisse--Sottile [NS16] on higher convexity of complements of tropical varieties, while providing a family of…
A tropical approach to a generalized Hodge conjecture for positive currents
Farhad Babaee, June Huh
Demailly showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear comb…
Complex Tropical Currents, Extremality, and Approximations
Farhad Babaee
To a tropical -cycle in , we naturally associate a normal closed and -dimensional current on denoted by $\mathscr{T}_n^p…