55 citations · 190 across the 23 of their papers we have counts for
29 papers
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,…
Towards the tropicalization of reductive groups
Desmond Coles, Martin Ulirsch
Let be a connected reductive algebraic group over an algebraically closed field of characteristic zero carrying the trivial valuation. In this article we discuss two candidates…
An Abel-Jacobi theorem for metrized complexes of Riemann surfaces
Maximilian C. E. Hofmann, Martin Ulirsch
Motivated by the recent surge of interest in the geometry of hybrid spaces, we prove an Abel-Jacobi theorem for a metrized complex of Riemann surfaces, generalizing both the classi…
Log-concavity for independent sets of valuated matroids
Jeffrey Giansiracusa, Felipe Rincón, Victoria Schleis +1
Recently, several proofs of the Mason--Welsh conjecture for matroids have been found, which asserts the log-concavity of the sequence that counts independent sets of a given size.…
Logarithmic concavity of bimatroids
Felix Röhrle, Martin Ulirsch
A bimatroid is a matroid-like generalization of the collection of regular minors of a matrix. In this article, we use the theory of Lorentzian polynomials to study the logarithmic…
Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization
Andreas Gross, Inder Kaur, Martin Ulirsch +1
Let be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semihomogeneous vector bundles on from the perspec…
Buildings, valuated matroids, and tropical linear spaces
Luca Battistella, Kevin Kuehn, Arne Kuhrs +2
Affine Bruhat--Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of parametrizes flags of subspaces/lattices in or,…
phenomena on abelian varieties
Barbara Bolognese, Alex Küronya, Martin Ulirsch
Let be a complex abelian variety. We prove an analogue of both the (cohomological) conjecture and the geometric conjecture connecting the finer topological structur…
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…
Tropicalization of the universal Jacobian
Margarida Melo, Samouil Molcho, Martin Ulirsch +1
In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process o…
Tropicalization of toric prevarieties
Alex Küronya, Pedro Souza, Martin Ulirsch
The homogeneous spectrum of a multigraded finitely generated algebra (in the sense of Brenner-Schröer) always admits an embedding into a toric variety that is not necessarily separ…
A non-Archimedean analogue of Teichmüller space and its tropicalization
Martin Ulirsch
In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue of Teichmüller space whose points are pa…
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…
Divisorial motivic zeta functions for marked stable curves
Madeline Brandt, Martin Ulirsch
We define a divisorial motivic zeta function for stable curves with marked points which agrees with Kapranov's motivic zeta function when the curve is smooth and unmarked. We show…
Abelian tropical covers
Yoav Len, Martin Ulirsch, Dmitry Zakharov
Let be a finite abelian group. In this article, we classify harmonic -covers of a tropical curve (which allow dilation along edges and at vertices)…
Skeletons of Prym varieties and Brill--Noether theory
Yoav Len, Martin Ulirsch
We show that the non-Archimedean skeleton of the Prym variety associated to an unramified double cover of an algebraic curve is naturally isomorphic (as a principally polarized tro…
Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective
Madeline Brandt, Martin Ulirsch
We show that the non-Archimedean skeleton of the -th symmetric power of a smooth projective algebraic curve is naturally isomorphic to the -th symmetric power of the trop…
Realizability of tropical canonical divisors
Martin Moeller, Martin Ulirsch, Annette Werner
We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability pr…
Clutching and gluing in tropical and logarithmic geometry
Alana Huszar, Steffen Marcus, Martin Ulirsch
The classical clutching and gluing maps between the moduli stacks of stable marked algebraic curves are not logarithmic, i.e. they do not induce morphisms over the category of loga…
A moduli stack of tropical curves
Renzo Cavalieri, Melody Chan, Martin Ulirsch +1
We contribute to the foundations of tropical geometry with a view towards formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose…
Towards a tropical Hodge bundle
Bo Lin, Martin Ulirsch
The moduli space of tropical curves of genus is a generalized cone complex that parametrizes metric vertex-weighted graphs of genus . For each such graph , t…
Logarithmic Picard groups, chip firing, and the combinatorial rank
Tyler Foster, Dhruv Ranganathan, Mattia Talpo +1
Illusie has suggested that one should think of the classifying group of -torsors on a logarithmically smooth curve over a standard logarithmic point as a logarithmic…
Non-Archimedean geometry of Artin fans
Martin Ulirsch
The purpose of this article is to study the role of Artin fans in tropical and non-Archimedean geometry. Artin fans are logarithmic algebraic stacks that can be described completel…
Skeletons and fans of logarithmic structures
Dan Abramovich, Qile Chen, Steffen Marcus +2
We survey a collection of closely related methods for generalizing fans of toric varieties, include skeletons, Kato fans, Artin fans, and polyhedral cone complexes, all of which ap…