42 citations · 172 across the 30 of their papers we have counts for
5 papers · 1 filter
Voronoi tilings, toric arrangements and degenerations of line bundles II
Omid Amini, Eduardo Esteves
We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relatio…
Voronoi tilings, toric arrangements and degenerations of line bundles I
Omid Amini, Eduardo Esteves
We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relatio…
Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class
Omid Amini, Matthieu Piquerez
This is a sequel to our work in tropical Hodge theory. Our aim here is to prove a tropical analogue of the Clemens-Schmid exact sequence in asymptotic Hodge theory. As an applicati…
Hodge theory for tropical varieties
Omid Amini, Matthieu Piquerez
In this paper we prove that the cohomology of smooth projective tropical varieties verify the tropical analogs of three fundamental theorems which govern the cohomology of complex…
Moduli of hybrid curves I: Variations of canonical measures
Omid Amini, Noema Nicolussi
The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves a…