# Analytic Projective Geometry

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*Eduardo Casas-Alvero*

A publication of the European Mathematical Society

Projective geometry is concerned with the properties of
figures that are invariant by projecting and taking sections. It is
considered one of the most beautiful parts of geometry and plays a
central role because its specializations cover the whole of the
affine, Euclidean and non-Euclidean geometries. The natural extension
of projective geometry is projective algebraic geometry, a rich and
active field of research. The results and techniques of projective
geometry are intensively used in computer vision.

This book contains a comprehensive presentation of projective
geometry, over the real and complex number fields, and its
applications to affine and Euclidean geometries. It covers central
topics such as linear varieties, cross ratio, duality, projective
transformations, quadrics and their classifications—projective,
affine and metric—as well as the more advanced and less usual
spaces of quadrics, rational normal curves, line complexes and the
classifications of collineations, pencils of quadrics and
correlations.

Two appendices are devoted to the projective foundations of
perspective and to the projective models of plane non-Euclidean
geometries. The book uses modern language, is based on linear algebra,
and provides complete proofs. Exercises are proposed at the end of
each chapter; many of them are beautiful classical results.

The material in this book is suitable for courses on projective
geometry for undergraduate students, with a working knowledge of a
standard first course on linear algebra. The text is a valuable guide
to graduate students and researchers working in areas using or related
to projective geometry, such as algebraic geometry and computer
vision, and to anyone looking for an advanced view of geometry as a
whole.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Undergraduate and graduate students and research mathematicians interested in projective geometry.

#### Reviews & Endorsements

... [A]n excellent reference source for people interested in the subject.

-- MAA Reviews