748 citations · 839 across the 24 of their papers we have counts for
13 papers · 1 filter
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…
Principal bundles on metric graphs: the case
Andreas Gross, Martin Ulirsch, Dmitry Zakharov
Using the notion of a root datum of a reductive group we propose a tropical analogue of a principal -bundle on a metric graph. We focus on the case , i.e. t…
Kirchhoff's theorem for Prym varieties
Yoav Len, Dmitry Zakharov
We prove an analogue of Kirchhoff's matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms…
Tropical double ramification loci
Martin Ulirsch, Dmitry Zakharov
Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in $\mat…