Singular Points of Complex Hypersurfaces

John Milnor

• Publisher: Princeton University Press
• Year: 2016
• Print ISBN: 9780691080659
• eBook ISBN: 9781400881819
• Topic: Mathematics
• Subtopic: Algebraic Geometry
• Index: Mathematics

Fields Medal–winning mathematician John Milnor's classic treatment of singular points of complex hypersurfaces

One of the greatest mathematicians of the twentieth century, John Milnor has made fundamental discoveries in diverse areas of mathematics, from topology and dynamical systems to algebraic K-theory. He is renowned as a master of mathematical exposition and his many books have become standard references in the field. Singular Points of Complex Hypersurfaces provides an incisive and authoritative study of the local behavior of a complex hypersurface V in Euclidean space at a singularity Z0.

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to publishing the major works of the new millennium.

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Preface
• CONTENTS
• §1. Introduction
• §2. Elementary facts about real or complex algebraic sets
• §3. The curve selection lemma
• §4. The fibration theorem
• §5. The topology of the fiber and of K
• §6. The case of an isolated critical point
• §7. The middle Betti number of the fiber
• §8. Is K a topological sphere?
• §9. Brieskorn varieties and weighted homogeneous polynomials
• §10. The classical case : curves in C^2
• §11. A fibration theorem for real singularities
• Appendix A. Whitney’s finiteness theorem for algebraic sets
• Appendix B. The multiplicity of an isolated solution of analytic equations
• Bibliography