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In the fall semester of 1979 I gave a course on deformation theory at Berkeley. My goal was to understand completely Grothendieck’s local study of the Hilbert scheme using the …
This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back ground in calculus, …
Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on …
The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties. This volume grew …
This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable …
This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the …
The aim of this book is to provide a guide to a rich and fascinating subject: algebraic curves, and how they vary in families. The revolution that the field of algebraic geometry …
For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating …
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in …
In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or …