Dmitry Zakharov

activity

20242026

collaborators

4 papers

math.AG2026

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 $R_{4} ⇢ A_{3}$ .

math.AG2025

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,…

math.AG2025

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 $I ¨ : I^ \to I^$ of tropical curves of genus $g(Î…

math.CO2024

Critical groups in harmonic abelian quotients

Mariia Vetluzhskikh, Dmitry Zakharov

A harmonic cover of graphs $p : X \to X$ induces a surjective pushforward morphism $p_{*} : Jac (X) \to Jac (X)$ on the critical groups.…