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Lectures on Curves, Surfaces and Projective Varieties
EMS Textbooks in Mathematics

Mauro C. Beltrametti (University of Genova, Italy)
Ettore Carletti (University of Genova, Italy)
Dionisio Gallarati (University of Genova, Italy)
Giacomo Monti Bragadin (University of Genova, Italy)

Lectures on Curves, Surfaces and Projective Varieties

A Classical View of Algebraic Geometry
First corrected reprint, June 2012

ISBN print 978-3-03719-064-7, ISBN online 978-3-03719-564-2
DOI 10.4171/064
August 2009, 506 pages, hardcover, 16.5 x 23.5 cm.
58.00 Euro

This book offers a wide-ranging 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 of the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses on 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.

Keywords: Algebraic geometry, projective varieties, curves, surfaces, special varieties

Further Information

Review in Zentralblatt MATH 1180.14001

Review in MR 2549804

Review in 2010oct CHOICE