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Titlebook: What is the Genus?; Patrick Popescu-Pampu Book 2016 Springer International Publishing Switzerland 2016 01A05, 14-03, 30-03, 55-03.Genus.Ri

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發(fā)表于 2025-3-21 19:10:43 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱What is the Genus?
編輯Patrick Popescu-Pampu
視頻videohttp://file.papertrans.cn/1028/1027821/1027821.mp4
概述Presents, through the works of the pioneers, the sophisticated evolution of one of the most important notions of geometry and topology.Features many illustrations which aid the understanding of the mo
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: What is the Genus?;  Patrick Popescu-Pampu Book 2016 Springer International Publishing Switzerland 2016 01A05, 14-03, 30-03, 55-03.Genus.Ri
描述Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena..
出版日期Book 2016
關(guān)鍵詞01A05, 14-03, 30-03, 55-03; Genus; Riemann surfaces; Algebraic varieties; Homology; Riemann-Roch theorem
版次1
doihttps://doi.org/10.1007/978-3-319-42312-8
isbn_softcover978-3-319-42311-1
isbn_ebook978-3-319-42312-8Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer International Publishing Switzerland 2016
The information of publication is updating

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沙發(fā)
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Newton and the Classification of Curves the “calculus of fluxions”, his version of the differential calculus. This partially explains why he undertook to classify the curves of degree three according to various species, in analogy with the classification of those of degree two, the .,into . or .. The following is the first paragraph of t
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發(fā)表于 2025-3-22 15:59:18 | 只看該作者
Jakob Bernoulli and the Construction of Curves“mechanical” or “transcendental” curves, that is, curves which are not “algebraic” (defined by a polynomial equation). Those methods created a common framework for Descartes’ algebraic curves and for the curves furnished by the differential and integral calculus:
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A Proof by Abelor instance in 1829, in the paper [3], he formulated the following version of the theorem cited in extenso in the previous chapter. This version makes no reference to the “number of algebraic relations” (and therefore to the genus)
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Abel’s Motivationsn form, a little like a secondary character remaining in the shadows, devoid of name. It is worth trying to understand better the general problems which preoccupied Abel at that time, of which [128] is only an expression. Happily for us, Abel wrote about these problems in an 1828 letter [2] to Legen
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A Reinterpretation of Abel’s Workscompletely prove them, he discovered many theorems concerning those relations. For instance, in [115] Kleiman lists and sketches modern proofs of the theorems he encountered in Abel’s paper [1]. One of the most famous such theorems, which is explained in nearly every textbook on algebraic curves and
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