We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is
naturally identified with the moduli space of extended tropical curves, and that this is …

We contribute to the foundations of tropical geometry with a view toward formulating tropical
moduli problems, and with the moduli space of curves as our main example. We propose a …

Let be an algebraically closed field which is complete with respect to a nontrivial, non-
Archimedean valuation and let be its value group. Given a smooth, proper, connected-curve …

We discuss linear series on tropical curves and their relation to classical algebraic geometry,
describe the main techniques of the subject, and survey some of the recent major …

We study the Berkovich analytification of the space of genus 0 logarithmic stable maps to a
toric variety X and present applications to both algebraic and tropical geometry. On …

We use recent results by Bainbridge–Chen–Gendron–Grushevsky–Möller on
compactifications of strata of abelian differentials to give a comprehensive solution to the …

For each universal genus‐g polarization μ of degree d, we construct a universal tropical
Jacobian J μ, gtrop as a generalized cone complex over the moduli space of stable pointed …

We compactify the classical moduli variety A g of principally polarized abelian varieties of
complex dimension g, by attaching the moduli of flat tori of real dimensions at most g in an …

We prove the quasimodularity of generating functions for counting torus covers, with and
without Siegel–Veech weight. Our proof is based on analyzing decompositions of flat …

We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is
naturally identified with the moduli space of extended tropical curves, and that this is …