Principles of Geometry, Volume 5

Front Cover
Cambridge University Press, Oct 31, 2010 - Mathematics - 262 pages
Henry Frederick Baker (1866-1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the fifth volume, describes the birational geometry of curves.
 

Contents

INTRODUCTORY ACCOUNT
1
Greatest possible number of double points of a plane curve 1011
10
Examples of elliptic curves Coresiduation Salmons
18
THE ELIMINATION OF THE MULTIPLE
24
Examples of transformation of curves 3134
31
The parametric expression of a branch of a curve 3943
39
General theorem for infinities of a rational function 4649
46
Examples of Abels theorem 5557
55
INTEGRALS RELATIONS AMONG PERIODS
136
Interchange of argument and parameter Converse of Abels
144
Important properties of the fundamental integral functions 151155
151
The functions reciprocal to the fundamental integral func
157
The structure of a certain fundamental rational function 165169
165
Explicit form of relation for interchange of argument
171
Some particular applications Return to theory of special
177
Interpretation of the formulae as illustrating general prin
192

MENTALS OF THE THEORY OF LINEAR SERIES
59
Equivalent or coresidual sets of points on the curve
65
Applications of the RiemannRoch formula Cliffords
78
The existence of a rational function with assigned poles
86
The theory of special sets an extension of Cliffords theorem
94
Related theorem as to intersections of plane curves 105107
105
THE PERIODS OF ALGEBRAIC INTEGRALS
111
Riemann surfaces 121124
121
Curve systems on a surface The EulerPoincare invariant 132133
132
Curves which are the complete intersection of two surfaces 201208
201
Curves which are the partial intersection of two surfaces 208209
208
Examples Curves not determinable by three surfaces
209
Examples Composite curve intersection of two surfaces
216
Another proof of the determination of the canonical series
226
The greatest genus possible for a curve of given order
234
Examples The form of the everywhere finite integrals
243
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