748 citations · 839 across the 24 of their papers we have counts for
28 papers
Resolution of the Prym map in genus 4
Dmitry Zakharov
We use the tropical trigonal construction to describe the minimal toroidal resolution of the Prym period map .
Tropical reductive groups and principal bundles on metric graphs
Andreas Gross, Arne Kuhrs, Martin Ulirsch +1
We propose an elementary tropical analogue of a reductive group that combines the datum of a Weyl group and the tropicalization of a fixed maximal torus. For the classical groups,…
The trigonal construction and the second moment of the tropical Prym variety
Dmitry Zakharov
We use the tropical trigonal construction to calculate the second moment of the tropical Prym variety of all double covers of tropical curves of genus $g(Γ)\le…
Critical groups in harmonic abelian quotients
Mariia Vetluzhskikh, Dmitry Zakharov
A harmonic cover of graphs induces a surjective pushforward morphism on the critical groups.…
A matroidal perspective on the tropical Prym variety
Felix Röhrle, Dmitry Zakharov
We associate a matroid to a harmonic double cover of metric graphs. The matroid is a geometric interpretation of Zaslavsk…
Chip-firing on graphs of groups
Margaret Meyer, Dmitry Zakharov
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 J…