This book resulted from two reports (published in 1928 and 1932) of the Committee on Rational Transformations, established by the National Research Council. The purpose of the reports was to give a comprehensive survey of the literature on the subject. Each chapter is regarded as a separate unit that can be read independently.

Readership

Graduate students and research mathematicians.

Table of Contents

• Quadratic cremona transformations
• Analysis of singularities of plane algebraic curves
• Linear systems of plane curves
• Planar cremona transformations
• Multiple correspondences between two planes
• Involutions on rational curves
• Correspondences on non-rational curves
• Cremona transformations in space and hyperspace
• \((1, 2)\) correspondences between \(S^{\prime}_r\) and \(S_r, r> 2\)
• Reduction of singularities of space curves and surfaces
• Multiple correspondence in space and hyperspace
• The mapping of a rational surface on a plane
• The mapping of a rational congruence on a plane
• Involutions on irrational surfaces
• Transcendental theory
• Singular correspondences between algebraic curves
• Hyperelliptic surfaces and abelian varieties

• Curves and ruled surfaces
• The mapping of systems of curves
• Systems of lines in \(S_n\); Irregular surfaces
• Cremona transformations
• Multiple correspondences
• Surfaces and varieties