Zobrazeno 1 - 10
of 177
pro vyhledávání: '"Zakharov, Dmitry"'
Autor:
Vetluzhskikh, Mariia, Zakharov, Dmitry
A harmonic cover of graphs $p:\widetilde{X}\to X$ induces a surjective pushforward morphism $p_*:\operatorname{Jac}(\widetilde{X})\to \operatorname{Jac}(X)$ on the critical groups. In the case when $p$ is Galois with abelian Galois group, we compute
Externí odkaz:
http://arxiv.org/abs/2409.04629
Autor:
Röhrle, Felix, Zakharov, Dmitry
We associate a matroid $M(\widetilde{\Gamma}/\Gamma)$ to a harmonic double cover $\pi:\widetilde{\Gamma}\to \Gamma$ of metric graphs. The matroid $M(\widetilde{\Gamma}/\Gamma)$ is a geometric interpretation of Zaslavsky's signed graphic matroid. We s
Externí odkaz:
http://arxiv.org/abs/2311.09872
Autor:
Meyer, Margaret, Zakharov, Dmitry
We define the Laplacian matrix and the Jacobian group of a finite graph of groups. We prove analogues of the matrix tree theorem and the class number formula for the order of the Jacobian of a graph of groups. Given a group $G$ acting on a graph $X$,
Externí odkaz:
http://arxiv.org/abs/2307.03348
Autor:
Ghosh, Arkabrata, Zakharov, Dmitry
We calculate the volume of the tropical Prym variety of a harmonic double cover of metric graphs having non-trivial dilation. We show that the tropical Prym variety behaves discontinuously under deformations of the double cover that change the number
Externí odkaz:
http://arxiv.org/abs/2303.03904
Autor:
Röhrle, Felix, Zakharov, Dmitry
We give a purely tropical analogue of Donagi's $n$-gonal construction and investigate its combinatorial properties. The input of the construction is a harmonic double cover of an $n$-gonal tropical curve. For $n = 2$ and a dilated double cover, the o
Externí odkaz:
http://arxiv.org/abs/2210.02267
Using the notion of a root datum of a reductive group $G$ we propose a tropical analogue of a principal $G$-bundle on a metric graph. We focus on the case $G=\mathrm{GL}_n$, i.e. the case of vector bundles. Here we give a characterization of vector b
Externí odkaz:
http://arxiv.org/abs/2206.10219
We analyse the detail of interactions of two-dimensional solitary waves called lumps and one-dimensional line solitons within the framework of the Kadomtsev-Petviashvili equation describing wave processes in media with positive dispersion. We show th
Externí odkaz:
http://arxiv.org/abs/2108.06071
We construct a broad class of solutions of the KP-I equation by using a reduced version of the Grammian form of the $\tau$-function. The basic solution is a linear periodic chain of lumps propagating with distinct group and wave velocities. More gene
Externí odkaz:
http://arxiv.org/abs/2102.07038