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- catalog abstract ""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."--Jacket.".
- catalog contributor b12218271.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog 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."--Jacket.".
- catalog description "1. Curves and Divisors on Algebraic Varieties -- 2. Parametrizing Morphisms -- 3. "Bend-and-Break" Lemmas -- 4. Uniruled and Rationally Connected Varieties -- 5. The Rational Quotient -- 6. The Cone of Curves in the Smooth Case -- 7. Cohomological Methods.".
- catalog description "Includes bibliographical references (p. [221]-228) and index.".
- catalog extent "xiii, 233 p. :".
- catalog identifier "0387952276 (alk. paper)".
- catalog isPartOf "Universitext".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "516.3/5 21".
- catalog subject "Geometry, Algebraic.".
- catalog subject "QA564 .D44 2001".
- catalog tableOfContents "1. Curves and Divisors on Algebraic Varieties -- 2. Parametrizing Morphisms -- 3. "Bend-and-Break" Lemmas -- 4. Uniruled and Rationally Connected Varieties -- 5. The Rational Quotient -- 6. The Cone of Curves in the Smooth Case -- 7. Cohomological Methods.".
- catalog title "Higher-dimensional algebraic geometry / Olivier Debarre.".
- catalog type "text".