# Lectures on Curves, Surfaces and Projective Varieties: A Classical View of Algebraic Geometry

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*Mauro C. Beltrametti; Ettore Carletti; Dionisio Gallarati; Giacomo Monti Bragadin*

Translated from the Italian by Francis Sullivan

A publication of the European Mathematical Society

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 & Endorsements

...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