120 citations · 251 across the 16 of their papers we have counts for
19 papers
Tropical moduli spaces of stable maps to a curve
Andreas Gathmann, Hannah Markwig, Dennis Ochse
We construct moduli spaces of rational covers of an arbitrary smooth tropical curve in R^r as tropical varieties. They are contained in the balanced fan parametrizing tropical stab…
Moduli spaces of curves in tropical varieties
Andreas Gathmann, Dennis Ochse
We describe a framework to construct tropical moduli spaces of rational stable maps to a smooth tropical hypersurface or curve. These moduli spaces will be tropical cycles of the e…
Realizability of Tropical Curves in a Plane in the Non-Constant Coefficient Case
Anna Lena Birkmeyer, Andreas Gathmann
Let X be a plane in a torus over an algebraically closed field K, with tropicalization the matroidal fan Sigma. In this paper we present an algorithm which completely solves the qu…
The Realizability of Curves in a Tropical Plane
Andreas Gathmann, Kirsten Schmitz, Anna Lena Winstel
Let E be a plane in an algebraic torus over an algebraically closed field. Given a balanced 1-dimensional fan C in the tropicalization of E, i.e. in the Bergman fan of the correspo…
Irreducible cycles and points in special position in moduli spaces for tropical curves
Andreas Gathmann, Franziska Schroeter
In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of n-marked rational tropical curves. We prove that Psi-classes and vital di…
Broccoli curves and the tropical invariance of Welschinger numbers
Andreas Gathmann, Hannah Markwig, Franziska Schroeter
In this paper we introduce broccoli curves, certain plane tropical curves of genus zero related to real algebraic curves. The numbers of these broccoli curves through given points…