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What is the Genus?

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Cover of 'What is the Genus?'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 The \(\gamma \acute{\varepsilon }\nu o\varsigma\) According to Aristotle
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    Chapter 2 Descartes and the New World of Curves
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    Chapter 3 Newton and the Classification of Curves
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    Chapter 4 When Integrals Hide Curves
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    Chapter 5 Jakob Bernoulli and the Construction of Curves
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    Chapter 6 Fagnano and the Lemniscate
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    Chapter 7 Euler and the Addition of Lemniscatic Integrals
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    Chapter 8 Legendre and Elliptic Functions
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    Chapter 9 Abel and the New Transcendental Functions
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    Chapter 10 A Proof by Abel
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    Chapter 11 Abel’s Motivations
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    Chapter 12 Cauchy and the Integration Paths
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    Chapter 13 Puiseux and the Permutations of Roots
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    Chapter 14 Riemann and the Cutting of Surfaces
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    Chapter 15 Riemann and the Birational Invariance of Genus
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    Chapter 16 The Riemann–Roch Theorem
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    Chapter 17 A Reinterpretation of Abel’s Works
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    Chapter 18 Jordan and the Topological Classification
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    Chapter 19 Clifford and the Number of Holes
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    Chapter 20 Clebsch and the Choice of the Term “Genus”
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    Chapter 21 Cayley and the Deficiency
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    Chapter 22 Noether and the Adjoint Curves
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    Chapter 23 Klein, Weyl, and the Notion of an Abstract Surface
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    Chapter 24 The Uniformization of Riemann Surfaces
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    Chapter 25 The Genus and the Arithmetic of Curves
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    Chapter 26 Several Historical Considerations by Weil
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    Chapter 27 And More Recently?
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    Chapter 28 The Beginnings of a Theory of Algebraic Surfaces
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    Chapter 29 The Problem of the Singular Locus
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    Chapter 30 A Profusion of Genera for Surfaces
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    Chapter 31 The Classification of Algebraic Surfaces
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    Chapter 32 The Geometric Genus and the Newton Polyhedron
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    Chapter 33 Singularities Which Do Not Affect the Genus
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    Chapter 34 Hodge’s Topological Interpretation of Genera
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    Chapter 35 Comparison of Structures
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    Chapter 36 Hilbert’s Characteristic Function of a Module
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    Chapter 37 Severi and His Genera in Arbitrary Dimension
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    Chapter 38 Poincaré and Analysis Situs
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    Chapter 39 The Homology and Cohomology Theories
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    Chapter 40 Elie Cartan and Differential Forms
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    Chapter 41 de Rham and His Cohomology
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    Chapter 42 Hodge and the Harmonic Forms
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    Chapter 43 Weil’s Conjectures
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    Chapter 44 Serre and the Riemann–Roch Problem
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    Chapter 45 New Ingredients
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    Chapter 46 Whitney and the Cohomology of Fibre Bundles
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    Chapter 47 Genus Versus Euler–Poincaré Characteristic
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    Chapter 48 Harnack and Real Algebraic Curves
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    Chapter 49 The Riemann–Roch–Hirzebruch Theorem
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    Chapter 50 The Riemann–Roch–Grothendieck Theorem
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Title
What is the Genus?
Published by
Springer International Publishing, January 2016
DOI 10.1007/978-3-319-42312-8
ISBNs
978-3-31-942311-1, 978-3-31-942312-8
Authors

Popescu-Pampu, Patrick, Patrick Popescu-Pampu

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Mendeley readers

The data shown below were compiled from readership statistics for 5 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 5 100%

Demographic breakdown

Readers by professional status Count As %
Professor 2 40%
Other 1 20%
Student > Master 1 20%
Student > Ph. D. Student 1 20%
Readers by discipline Count As %
Mathematics 3 60%
Philosophy 1 20%
Physics and Astronomy 1 20%