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Lectures on Curves, Surfaces and Projective Varieties: A Classical View of Algebraic Geometry
Mauro C. Beltrametti, Ettore Carletti, Dionisio Gallarati, and Giacomo Monti Bragadin, University of Genova, Italy
Translated from the Italian by Francis Sullivan
A publication of the European Mathematical Society.
cover
EMS Textbooks in Mathematics
2009; 506 pp; hardcover
Volume: 9
ISBN-10: 3-03719-064-7
ISBN-13: 978-3-03719-064-7
List Price: US$78
Member Price: US$62.40
Order Code: EMSTEXT/9
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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 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
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