Kummer's Quartic Surface

Ronald William Henry Turnbull Hudson

University Press, 1905 - Functions, Theta - 222 pages

Contents

• CHAPTER: 1
• CHAPTER II: 14
• The shape of the surface: 21
• Connection between matrices and quaternions: 27
• SECT PAGE 15 The sixteen linear forms: 28
• Quadratic relations: 30
• The ten fundamental quadrics: 32
• The six fundamental complexes: 33
• Irrational equations of Kummers surface: 34
• CHAPTER IV: 37
• Apolar complexes: 38
• Groups of three and four apolar complexes: 39
• Six apolar complexes: 40
• Ten fundamental quadrics: 41
• Kleins 6015 configuration: 42
• Kummers 166 configuration: 44
• Line coordinates: 45
• Fundamental quadrics: 47
• Fundamental tetrahedra: 48
• CHAPTER V: 51
• Outline of the algebraical theory: 53
• Elliptic coordinates: 55
• Conjugate sets: 56
• Kleins tetrahedra: 57
• Relations of lines to: 58
• Asymptotic curves: 60
• Principal asymptotic curves: 62
• The congruence of second order and class: 63
• Relation between and A: 65
• Confocal congruences: 66
• CHAPTER VI: 68
• Equations of the complex and the complex surface: 69
• Singularities of the surface: 71
• The polar line: 72
• Shape of the surface: 73
• CHAPTER VII: 75
• Comparison of notations: 76
• Pairs and octads: 77
• Eighty Rosenhain odd tetrads: 78
• Sixty Göpel even tetrads: 79
• Odd and even hexads: 80
• CHAPTER VIII: 81
• The equation referred to a Rosenhain tetrahedron: 83
• Nodal quartic surfaces: 86
• CHAPTER IX: 89
• Multiple tetrahedroids: 91
• Battaglinis harmonic complex: 94
• Limiting forms: 98
• CHAPTER X: 100
• Apsidal surfaces: 101
• Singularities of the Wave Surface: 102
• Parametric representation: 104
• Tangent planes: 106
• The four parameters: 108
• Curvature: 109
• Asymptotic lines: 110
• Painvins complex: 112
• CHAPTER XI: 115
• Six real fundamental complexes: 118
• Equations of surfaces Ia Ib Ic: 121
• Four real and two imaginary complexes: 122
• Two real and four imaginary complexes: 125
• Six imaginary complexes: 126
• CHAPTER XII: 127
• Construction of the 156 configuration from six points in four dimensions: 129
• Analytical methods: 130
• The 16 configuration: 131
• General theory of varieties: 132
• Space sections of a certain quartic variety: 134
• CHAPTER XIII: 137
• Algebraic curves on Kummers surface: 138
• The eequation of a curve: 141
• General theorems on curves: 142
• Classification of families of curves: 145
• Linear systems of curves: 146
• CHAPTER XIV: 149
• Quartics through the same even tetrad: 151
• Quartics through the same odd tetrad: 153
• Sextics through six nodes: 154
• Sextics through ten nodes: 157
• Octavic curves through eight nodes: 158
• Octavic curves through sixteen nodes: 159
• CHAPTER XV: 160
• Transformation of Kummers surface: 162
• Quartic surfaces into which Kummers surface can be trans formed: 165
• Weddles surface: 166
• Equation of Weddles surface: 169
• CHAPTER XVI: 173
• Definition of theta functions: 175
• Characteristics and periods: 176
• Identical relations among the double theta functions: 179
• Parametric expression of Kummers surface: 180
• Theta functions of higher order: 182
• Sketch of the transcendental theory: 184
• CHAPTER XVII: 188
• Collinear points: 190
• Asymptotic curves: 194
• Inscribed configurations: 196
• CHAPTER XVIII: 200
• Transformation of theta functions: 201
• The invariant: 203
• Parametric curves: 204
• Unicursal curves: 206
• Geometrical interpretation of the singular relation kr121: 208
• Intermediary functions: 210
• Singular curves: 212
• Singular surfaces with invariant 5: 213
• Singular surfaces with invariant 8: 214
• Birational transformations of Kummer surfaces into themselves: 216
• INDEX: 221

Bibliographic information

• Title: Kummer's Quartic Surface
• Author: Ronald William Henry Turnbull Hudson
• Contributor: Henry Frederick Baker
• Publisher: University Press, 1905
• Original from: the University of California
• Digitized: Nov 21, 2008
• Length: 222 pages