Elimination Theory for Tropical Varieties
نویسندگان
چکیده
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
منابع مشابه
Nonarchimedean geometry, tropicalization, and metrics on curves
We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical multiplicities and a generalization of the Sturmfels–Tevelev multiplicity formula in tropical elimination theory to the case of a nontrivial valuation. For curves, we explore in detail the relationship between skeletal ...
متن کاملTropical Intersection Theory from Toric Varieties
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 and ordinary Chow cohomology classes on complete toric varieties. These objects fit into the framework of tropical intersection theory developed by Allermann and Rau. Standard facts about intersection theory on ...
متن کاملPhD project offering: tropical scheme theory
Tropical geometry has burgeoned in the decade and a half since its coalescence as a field of study. It is a combinatorialization of algebraic geometry, associating to each algebraic variety a so-called tropical variety, a polyhedral complex that is its combinatorial “shadow”. In the simplest cases tropical geometry can be seen as the algebraic geometry over the tropical semiring T = (R ∪ {∞}, m...
متن کاملA Tropical Toolkit
We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of degenerations of varieties using projective not-necessarily-normal toric varieties. The second part is a foundational account of tropical intersection theory ...
متن کاملThe Diagonal of Tropical Matroid Varieties and Cycle Intersections
We define an intersection product of tropical cycles on matroid varieties (via cutting out the diagonal) and show that it is well-behaved. In particular, this enables us to intersect cycles on moduli spaces of tropical rational marked curves Mn and Mlab n (∆,Rr). This intersection product can be extended to smooth varieties (whose local models are matroid varieties). We also study pull-backs of...
متن کامل