1 citations · 1 across the 2 of their papers we have counts for
4 papers
Hodge theory on tropical curves
Yury Eliyashev
We construct an analog of the Hodge theory on complex manifolds on tropical curves. We use the analytical approach to the problem, it is based on language of tropical differential…
Geometry of generalized amoebas
Yury Eliyashev
Recently Krichever proposed a generalization of the amoeba and the Ronkin function of a plane algebraic curve. In our paper higher-dimensional version of this generalization is stu…
Mixed Hodge structure on complements of complex coordinate subspace arrangements
Yury V. Eliyashev
We compute the mixed Hodge structure on the cohomology ring of complements of complex coordinate subspace arrangements. The mixed Hodge structure can be described in terms of the s…
The Hodge filtration on complements of complex coordinate subspace arrangements and integral representations of holomorphic functions
Yury Eliyashev
We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of ho…