EMS Textbooks in Mathematics 2009; 506 pp; hardcover Volume: 9 ISBN10: 3037190647 ISBN13: 9783037190647 List Price: US$78 Member Price: US$62.40 Order Code: EMSTEXT/9
 This book offers a wideranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Undergraduate and graduate students interested in algebraic geometry. Reviews "...experts will readily detect how the modern viewpoint really informs these authors' approach, the better to smooth any future transition for students first entering the subject."  D.V. Feldman, Choice Table of Contents  Prerequisites
 Algebraic sets, morphisms, and rational maps
 Geometric properties of algebraic varieties
 Rudiments of elimination theory
 Hypersurfaces in projective space
 Linear systems
 Algebraic curves
 Linear series on algebraic curves
 Cremona transformations
 Rational surfaces
 Segre varieties
 Grassmann varieties
 Supplementary exercises
 Bibliography
 Index
