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Search Results: 1 - 10 of 10072 matches for " Simon Hampe "
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A-Tint: A polymake extension for algorithmic tropical intersection theory
Simon Hampe
Mathematics , 2012, DOI: 10.1016/j.ejc.2013.10.001
Abstract: In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study of moduli spaces, where the underlying combinatorics of the varieties involved allow a much more efficient way of computing certain tropical cycles. The algorithms discussed here have been implemented in an extension for polymake, a software for polyhedral computations.
Combinatorics of tropical Hurwitz cycles
Simon Hampe
Mathematics , 2014, DOI: 10.1007/s10801-015-0615-0
Abstract: We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study how Hurwitz cycles can be written as divisors of rational functions and show that they are numerically equivalent to a tropical version of a representation as a sum of boundary divisors. The results and counterexamples in this paper were obtained with the help of a-tint, an extension for polymake for tropical intersection theory.
Tropical linear spaces and tropical convexity
Simon Hampe
Mathematics , 2015,
Abstract: In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the converse is true: Each tropical variety that is also tropically convex is supported on the complex of a valuated matroid. We also prove a tropical local-to-global principle: Any closed, connected, locally tropically convex set is tropically convex.
Universal families of rational tropical curves
Georges Francois,Simon Hampe
Mathematics , 2011, DOI: 10.4153/CJM-2011-097-0
Abstract: We introduce the notion of families of n-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of n-marked abstract rational tropical curves.
On rational equivalence in tropical geometry
Lars Allermann,Simon Hampe,Johannes Rau
Mathematics , 2014, DOI: 10.4153/CJM-2015-036-0
Abstract: This article discusses the concept of rational equivalence in tropical geometry (and replaces the older and imperfect version arXiv:0811.2860). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties. We then compute the "bounded" Chow groups of $\mathbb{R}^n$ by showing that they are isomorphic to the group of fan cycles. The main step in the proof is of independent interest: We show that every tropical cycle in $\mathbb{R}^n$ is a sum of (translated) fan cycles. This also proves that the intersection ring of tropical cycles is generated in codimension 1 (by hypersurfaces).
Moduli spaces of rational weighted stable curves and tropical geometry
Renzo Cavalieri,Simon Hampe,Hannah Markwig,Dhruv Ranganathan
Mathematics , 2014,
Abstract: We study moduli spaces of rational weighted stable tropical curves, and their connections with the classical Hassett spaces. Given a vector $w$ of weights, the moduli space of tropical $w$-stable curves can be given the structure of a balanced fan if and only if $w$ has only heavy and light entries. In this case, we can express the moduli space as the Bergman fan of a graphic matroid. Furthermore, we realize the tropical moduli space as a geometric tropicalization, and as a Berkovich skeleton, of the classical moduli space. This builds on previous work of Tevelev, Gibney--Maclagan, and Abramovich--Caporaso--Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fiber products of unweighted spaces, and explore parallels with the algebraic world.
Seymour Menton, Latin America's New Historical Novel
Teodoro Hampe Martínez
Lexis , 1994,
Abstract: SEYMOUR, MENTON. Latin America's New Historical Novel. Austin: University of Texas Press, 1993. x, 228 p. (Texas Pan American Series). ISBN 0-292-75157-5.
Humboldt y el mar peruano Una exploración de su travesía de Lima a Guayaquil (1802/1803)
Teodoro Hampe Martínez
HiN. Alexander von Humboldt im Netz , 2007,
Abstract: Article in Spanish, Abstract in Spanish
José Durand, Bibliófilo (su colección de libros y papeles en la Universidad de Notre Dame)
Hampe Martínez, Teodoro
Revista de Indias , 1997,
Carlos Montúfar y Larrea (1780-1816), el quite o compa ero de Humboldt
Hampe Martínez, Teodoro
Revista de Indias , 2002,
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