arXiv:0704.3471v1 [math.AG] 26 Apr 2007 Page 1 arXiv:0704.3471v1 [math.AG] 26 Apr 2007
ELIMINATION THEORY FOR TROPICAL VARIETIES BERND STURMFELS AND JENIA …

We explain how logarithmic structures select principal components in an intersection of
schemes. These manifest in Chow homology and can be understood using strict transforms …

We apply ideas from intersection theory on toric varieties to tropical intersection theory. We
introduce mixed Minkowski weights on toric varieties which interpolate between equivariant …

We show how to equip the cone complexes of toroidal embeddings with additional structure
that allows to define a balancing condition for weighted subcomplexes. We then proceed to …

Let X be a complete toric variety. If L is a line bundle on X, then various positivity properties
of L admit explicit interpretations in terms of convex geometry. These interpretations can be …

The prototypical examples of tropical compactifications are compactifications of
complements of hyperplane arrangements, which posses a number of remarkable …

Matroids are combinatorial abstractions of independence, a ubiquitous notion that pervades
many branches of mathematics. June Huh and his collaborators recently made spectacular …

An enumerative problem on a variety V is usually solved by reduction to intersection theory
in the cohomology of a compactification of V. However, if the problem is invariant under a …

We prove a Poincaré duality for the Chow rings of smooth fans whose support are tropical
linear spaces. As a consequence, we show that cycles and cocycles on tropical manifolds …

The third author introduced the $ g $-polynomial $ g_M (t) $ of a matroid, a covaluative
matroid statistic which is unchanged under series and parallel extension. The $ g …