Kummer's Quartic Surface

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Contents

Equations of surfaces c
121
Four real and two imaginary complexes
122
H F BAKER
123
Two real and four imaginary complexes
125
Six imaginary complexes
126
CHAPTER XII
127
Construction of the 150 configuration from six points in four dimensions
129
Analytical methods
130
The 168 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 Qequation 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
163
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 r12 l
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

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