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Journals and Conferences
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study of moduli spaces, where the underlying combinatorics of the varieties involved allow a much more efficient way of… (More)
This article discusses the concept of rational equivalence in tropical geometry (and replaces the older and imperfect version [AR08]). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties. We then compute the “bounded” Chow groups of R by showing that they are isomorphic to the group of… (More)
We introduce the notion of families of n-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of n-marked abstract rational tropical curves Mn.
In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations.… (More)
We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study… (More)
We study a particular graded ring structure on the set of all loopfree matroids on a fixed labeled ground set, which occurs naturally in tropical geometry. The product is given by matroid intersection and the additive structure is defined by assigning to each matroid the indicator vector of its chains of flats. We show that this ring is generated in corank… (More)
We describe an XML file format for storing data from computations in algebra and geometry. We also present a formal specification based on a RELAX-NG schema.