منابع مشابه
Lifting Tropical Intersections
We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations intersect in the expected dimension. We also prove a similar result for intersections inside an ambient subvariety of the torus, when the tropicalizations meet inside a facet of multiplicity 1. The proof...
متن کاملLifting Non-proper Tropical Intersections
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 component C of Trop(X) ∩ Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a s...
متن کاملLifting Tropical Bitangents
We study lifts of tropical bitangents to the tropicalization of a given complex algebraic curve together with their lifting multiplicities. Using this characterization, we show that generically all the seven bitangents of a smooth tropical plane quartic lift in sets of four to algebraic bitangents. We do this constructively, i.e. we give solutions for the initial terms of the coefficients of th...
متن کاملIntersections on Tropical Moduli Spaces
This article tries to answer the question: How far can the algebro-geometric theory of rational descendant Gromov-Witten invariants be carried over to the tropical world? Given the fact that our moduli spaces are non-compact, the answer is surprisingly positive: We discuss universal families and the string, divisor and dilaton equations, we prove a splitting lemma describing the intersection wi...
متن کاملTropical Intersections and Rational Functions on Graphs
This write-up is concerned with the intersections of tropical curves and their relationship to rational functions on graphs. It is based on projects for Bernd Sturmfel’s 255 course in Fall 2011, Martin Olsson’s 256B course in Spring 2012, and work with Matt Baker. Sections 2 and 3 run through previous results on tropical intersections in the transverse and non-transverse cases, respectively. Se...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2019.105138