XXIV 
CONTENTS 
§ 5. Transformations in one plane 
Isologous transformations ....... 459 
Curves of fixed points . . . . . . . .461 
Ai-curves and N-curves ........ 464 
Fixed points of two sorts . . . . . . .466 
CHAPTER VII 
TYPES OF CREMONA TRANSFORMATIONS 
§ 1. Types of lowest order 
Determination of all types of order 7 or less .... 468 
Table of types ......... 470 
§ 2. Numerical relations 
Symmetric types . . . . . . , . .470 
Limits for number of fundamental points . . . .471 
§ 3. Transformations with curves of fixed' points 
Simplest transformations with curves of fixed points . . .474 
Transformations with curves of fixed points of genus greater than 1 475 
§ 4. Involutory transformations 
Symmetric involutory transformations . , . . .478 
Other involutory transformations . . . . . .479 
Involutory transformations of lowest class .... 482 
§ 5. Cremona transformations and integral collineations in hyperspace 
Integral collineations associated with Cremona transformations . 483 
Kantor’s theorem for necessary and sufficient conditions . . 485 
Collineations corresponding to familiar transformations . . 487 
CHAPTER VIII 
GROUPS OF CREMONA TRANSFORMATIONS 
§ 1. Continuous groups 
General properties of continuous groups . . . . .489 
Enriques’s theorem ........ 490 
§ 2. Infinite discontinuous groups 
General considerations . . . . . . . .492 
Groups with invariant hyperelliptic curves . . . .493 
§ 3. Finite groups 
Determination of finite groups by invariant linear systems. . 496 
INDEX OF AUTHORS QUOTED 499 
SUBJECT INDEX 511