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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Book 2016ration, 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

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Descartes and the New World of CurvesLet us make a huge temporal leap, in order to reach the “.” [56] of Descartes, published in 1637, illustrating his “.”.

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When Integrals Hide CurvesIn the two previous chapters we dealt with curves and the polynomials defining them or the mechanisms generating them. Those curves often represented incarnations of problems involving polynomial equations, with one or more variables.

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Cauchy and the Integration PathsIn Chap. 9, we saw the genus timidly appearing in Abel’s investigations concerning so-called .. Let us concentrate now on the definition of such an integral.

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