20 citations · 87 across the 14 of their papers we have counts for
17 papers
Tailoring a pair of pants: the phase tropical version
Ilia Zharkov
We show that the phase tropical pair-of-pants is (ambient) isotopic to the complex pair-of-pants. This paper can serve as an addendum to the author's joint paper with Ruddat arXiv:…
Compactifying torus fibrations over integral affine manifolds with singularities
Helge Ruddat, Ilia Zharkov
This is an announcement of the following construction: given an integral affine manifold with singularities, we build a topological space which is a torus fibration over $B…
Tropical Abelian varieties, Weil classes and the Hodge Conjecture
Ilia Zharkov
We describe in some details an idea of M. Kontsevich how one can try to find a counterexample to the Hodge conjecture using tropical geometry.
Tailoring a pair of pants
Helge Ruddat, Ilia Zharkov
We show how to deform the map such that the image of the complex pair of pants is…
Phase tropical hypersurfaces
Gabriel Kerr, Ilia Zharkov
We prove that a generic smooth complex hypersurface in the complex torus is homeomorphic to the corresponding phase tropical hypersurface.
Tropical Homology
Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin +1
Given a tropical variety X and two non-negative integers p and q we define homology group . We show that if X is a smooth tropical variety that can be represented as th…