Synopses & Reviews
Students and teachers will welcome the return of this unabridged reprint of one of the first English-language texts to offer full coverage of algebraic plane curves. It offers advanced students a detailed, thorough introduction and background to the theory of algebraic plane curves and their relations to various fields of geometry and analysis.
The text treats such topics as the topological properties of curves, the Riemann-Roch theorem, and all aspects of a wide variety of curves including real, covariant, polar, containing series of a given sort, elliptic, hyperelliptic, polygonal, reducible, rational, the pencil, two-parameter nets, the Laguerre net, and nonlinear systems of curves. It is almost entirely confined to the properties of the general curve rather than a detailed study of curves of the third or fourth order. The text chiefly employs algebraic procedure, with large portions written according to the spirit and methods of the Italian geometers. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace.
Readers will find this volume ample preparation for the symbolic notation of Aronhold and Clebsch.
A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Table of Contents
The Fundamental Properties of Polynomials.
Elementary Properties of Curves.
Real Circuits of Curves.
Elementary Invariant Theory.
Projective Theory of Singular Points.
Metrical Properties of Curves.
The Singular Points.
The Reduction of Singularities.
Development in Series.
Systems of Points on a Curve.
General Theory of Linear Series.
Moduli and Limiting Values.
Singular Points of Correspondences.
Nonlinear Series of Groups of Points on a Curve.
Higher Theory of Correspondences.
Parametric Representation of the General Curve.
Postulation of Linear Systems by Points.
The Cremona Transformation.