共查询到20条相似文献,搜索用时 15 毫秒
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Aron Lagerberg 《Mathematische Zeitschrift》2012,270(3-4):1011-1050
We introduce the formalism of positive super currents on ${\mathbb{R}^{n}}$ , in strong analogy with the theory of positive currents in ${\mathbb{C}^{n}}$ . We consider intersection of currents and Lelong numbers, and as an application we show that the formalism can be used to describe tropical varieties. This is similar in spirit to the fact that in complex analysis the current of integration of an analytic variety can be identified with a closed, positive current. 相似文献
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Oleg Viro 《Japanese Journal of Mathematics》2008,3(2):185-214
Hilbert’s problem on the topology of algebraic curves and surfaces (the sixteenth problem from the famous list presented at
the second International Congress of Mathematicians in 1900) was difficult to formulate. The way it was formulated made it
difficult to anticipate that it has been solved. In the first part of the paper the history of the sixteenth Hilbert problem
and its solution is presented. The second part of the paper traces one of the ways in which tropical geometry emerged.
This article is based on the 4th Takagi Lectures that the author delivered at Kyoto University
on June 21, 2008. 相似文献
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Recently, Baker and Norine have proven a Riemann–Roch theorem for finite graphs. We extend their results to metric graphs
and thus establish a Riemann–Roch theorem for divisors on (abstract) tropical curves. 相似文献
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Alana Huszar Steffen Marcus Martin Ulirsch 《Journal of Pure and Applied Algebra》2019,223(5):2036-2061
The classical clutching and gluing maps between the moduli stacks of stable marked algebraic curves are not logarithmic, i.e. they do not induce morphisms over the category of logarithmic schemes, since they factor through the boundary. Using insight from tropical geometry, we enrich the category of logarithmic schemes to include so-called sub-logarithmic morphisms and show that the clutching and gluing maps are naturally sub-logarithmic. Building on the recent framework developed by Cavalieri, Chan, Wise, and the third author, we further develop a stack-theoretic counterpart of these maps in the tropical world and show that the resulting maps naturally commute with the process of tropicalization. 相似文献
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Arsalan Wares 《International Journal of Mathematical Education in Science & Technology》2013,44(2):264-272
The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to maximize the surface area and the volume. 相似文献
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Andreas Gathmann 《Advances in Mathematics》2008,217(2):537-560
Using Gromov-Witten theory the numbers of complex plane rational curves of degree d through 3d−1 general given points can be computed recursively with Kontsevich's formula that follows from the so-called WDVV equations. In this paper we establish the same results entirely in the language of tropical geometry. In particular this shows how the concepts of moduli spaces of stable curves and maps, (evaluation and forgetful) morphisms, intersection multiplicities and their invariance under deformations can be carried over to the tropical world. 相似文献
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Andreas Vohns 《ZDM》2006,38(6):498-504
“Basic ideas” (or “fundamental ideas” etc.) have been discussed in mathematical curriculum theory for about forty years. This paper will centre on the hypothesis that this concept can only be applied successfully by using it as a category for the analysis of concrete mathematical problems. This hypothesis will be illustrated by means of a sample problem from the Austrian Standards for Mathematics Education (“Bildungsstandards”). In this example, basic ideas are used in a content matter analysis which takes students' solutions to the problem as a starting point for the creation of a potentially substantial learning environment in trigonometry. 相似文献
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James Borger 《Mathematische Annalen》2011,351(4):877-933
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I. Sushko L. Gardini V. Avrutin 《Journal of Difference Equations and Applications》2016,22(12):1816-1870
The main purpose of the present survey is to contribute to the theory of dynamical systems defined by one-dimensional piecewise monotone maps. We recall some definitions known from the theory of smooth maps, which are applicable to piecewise smooth ones, and discuss the notions specific for the considered class of maps. To keep the presentation clear for the researchers working in other fields, especially in applications, many examples are provided. We focus mainly on the notions and concepts which are used for the investigation of various kinds of attractors of a map and related bifurcation structures observed in its parameter space. 相似文献
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V. P. Maslov 《Mathematical Notes》2015,98(5-6):798-804
A generalization of tropical geometry to the case of mixtures of ideal liquids and an increase in the number of prohibitions is presented. In addition to the well-known notions of skeleton and ameba, new notions of circulatory system and joints (angles in the skeleton) are introduced. 相似文献
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Sehie Park 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2439-2447
In the KKM theory, some authors adopt the concepts of the compact closure (ccl), compact interior (cint), transfer compactly closed-valued multimap, transfer compactly l.s.c. multimap, and transfer compactly local intersection property, respectively, instead of the closure, interior, closed-valued multimap, l.s.c. multimap, and possession of a finite open cover property. In this paper, we show that such adoption is inappropriate and artificial. In fact, any theorem with a term with “transfer” attached is equivalent to the corresponding one without “transfer”. Moreover, we can invalidate terms with “compactly” attached by giving a finer topology on the underlying space. In such ways, we obtain simpler formulations of KKM type theorems, Fan-Browder type fixed point theorems, and other results in the KKM theory on abstract convex spaces. 相似文献
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We discuss infinite elation generalized quadrangles as group coset geometries and use this approach to deal with the special case of those associated with flocks of quadratic cones of PG(3,K).This research begun while the second author was a C.N.R. visiting professor in Italy during May–June 1996. 相似文献
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