34 citations · 42 across the 8 of their papers we have counts for
9 papers
Novikov equations for commuting differential operators of orders 3,4,5
G. B. Shabat, V. V. Sokolov, A. V. Tsiganov
We consider Novikov equations for commutative ring generated by differential operators of orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method…
Fullerenes and Belyi functions
Nikolai M. Adrianov, George B. Shabat
The paper is an attempt to apply the theory of dessins d'enfants to the theory of fullerenes. The classical results concerning the calculation of the dodecahedron Belyi function ar…
Square-tiled surfaces and curves over number fields
George B. Shabat
The paper presents an analog of the old result by the author and V. Voevodsky, according to which a Riemann surface admits a conformal structure, defined by an equilateral triangul…
Belyi pairs in the critical filtrations of Hurwitz spaces
George Shabat
The \it critical filtration \rm of a Hurwitz space stratifies it according to the number of the critical values; the \it Belyi pairs \rm (three critical values) are considered as t…
Poincare polynomial for the moduli space and the number of points in
N. Amburg, E. Kreines, G. Shabat
We obtain a combinatorial proof that the number of points of the space satisfies the recurrent formula for Poincare polynomials of th…
On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves
Petr Dunin-Barkowski, Alexander Popolitov, George Shabat +1
We suggest a general method of computation of the homology of certain smooth covers of moduli spaces $\mathcal{M}_{g,1}\br{\mathbb{C}}$ of poi…
On the three-term curves
George B. Shabat, Alexei Sleptsov
We classify projective plane nonsingular curves admitting a 3-term presentation; they exist in any degree, generally constitute 5 birational families and are defined over rational…
Catalog of dessins d'enfants with \le 4 edges
N. M. Adrianov, N. Ya. Amburg, V. A. Dremov +5
In this work all the dessins d'enfant with no more than 4 edges are listed and their Belyi pairs are computed. In order to enumerate all dessins the technique of matrix model compu…
On the Chekhov-Fock coordinates of dessins d'enfants
G. Shabat, V. Zolotarskaia
There are several ways to associate a complex structure to a ribbon graph. In the construction of dessins d'enfants a single riemann surface is associated to each graph. We call it…