10 citations · 17 across the 5 of their papers we have counts for
6 papers
Vertex-Maximal Lattice Polytopes Contained in 2-Simplices
Jan-Philipp Litza, Christoph Pegel, Kirsten Schmitz
Motivated by the problem of bounding the number of rays of plane tropical curves we study the following question: Given and a unimodular -simplex what is th…
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…
Lower Bounds for the Number of Generic Initial Ideals
Joke Frels, Kirsten Schmitz
Given a graded ideal in a polynomial ring over a field it is well known, that the number of distinct generic initial ideals of is finite. While it is known that for a g…
Generic Tropical Varieties on Subvarieties and in the Non-constant Coefficient Case
Kirsten Schmitz
In earlier papers it was shown that the generic tropical variety of an ideal can contain information on algebraic invariants as for example the depth in a direct way. The existence…
Algebraic Properties of Generic Tropical Varieties
Tim Roemer, Kirsten Schmitz
We show that the algebraic invariants multiplicity and depth of a graded ideal in the polynomial ring are closely connected to the fan structure of its generic tropical variety in…
Generic Tropical Varieties
Tim Roemer, Kirsten Schmitz
We show that in the constant coefficient case the generic tropical variety of a graded ideal exists. This can be seen as the analogon to the existence of the generic initial ideal…