منابع مشابه
Tropical complete intersection curves
A tropical complete intersection curve C ⊆ Rn+1 is a transversal intersection of n smooth tropical hypersurfaces. We give a formula for the number of vertices of C given by the degrees of the tropical hypersurfaces. We also compute the genus of C (defined as the number of independent cycles of C) when C is smooth and connected. 1 Notation and definitions We work over the tropical semifield Rtr=...
متن کاملAlgebraic and Tropical Intersection Numbers
We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...
متن کاملOn Finding Ordinary Intersection Points∗
An algorithm is demonstrated that finds an ordinary intersection in an arrangement of n lines in R, not all parallel and not all passing through a common point, in time O(n logn). The algorithm is then extended to find an ordinary intersection among an arrangement of hyperplanes in R, no d passing through a line and not all passing through the same point, again, in time O(n logn). Two additiona...
متن کاملChapter 8 : Distinct intersection points
Claim 1.1. Let L be a set of n lines in R. Then there exists a nontrivial polynomial f ∈ R[x1, x2, x3] of degree smaller than 3 √ n that vanishes on all the lines of L. Proof. Let P be a set of at most 4n points, that is obtained by arbitrarily choosing 4 √ n points from every line of L. Since ( 3 √ n+3 3 ) > 4n, by Lemma 2.1 of Chapter 5 there exists a nontrivial polynomial f ∈ R[x1, x2, x3] o...
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 ...
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ژورنال
عنوان ژورنال: Collectanea Mathematica
سال: 2014
ISSN: 0010-0757,2038-4815
DOI: 10.1007/s13348-014-0118-7