Higher-Dimensional Algebraic Geometry
Publisher: Springer
Published: June 26, 2001
Language: eng
Number of pages: 248
ISBN-13: 9780387952277
First sentence: In this preliminary chapter (as well as in the next), we gather standard material that will be used throughout the book.
Description: "Higher-Dimensional Algebraic Geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author's goal is to provide an easily accessible introduction to the subject.

Based on lectures given at Harvard University, the book begins with preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps toward Mori's minimal model program of classification of algebraic varieties by proving the cone and contraction theorems."--BOOK JACKET.