© 2016

Projective Geometry

Solved Problems and Theory Review


  • Offers more than 200 problems with detailed solutions, helping the reader to "learn by doing"

  • The concise summary of the theory provides an overall view of the subject, highlighting the most important points

  • Uses simple and modern language for better readability


Part of the UNITEXT book series (UNITEXT, volume 104)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 104)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Elisabetta Fortuna, Roberto Frigerio, Rita Pardini
    Pages 1-60
  3. Elisabetta Fortuna, Roberto Frigerio, Rita Pardini
    Pages 61-105
  4. Elisabetta Fortuna, Roberto Frigerio, Rita Pardini
    Pages 107-171
  5. Elisabetta Fortuna, Roberto Frigerio, Rita Pardini
    Pages 173-261
  6. Back Matter
    Pages 263-266

About this book


This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of elementary Linear Algebra.


Projective spaces Projective transformations Conics Quadrics Plane curves

Authors and affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly
  3. 3.Dipartimento di MatematicaUniversità di PisaPisaItaly

About the authors

Elisabetta Fortuna was born in Pisa in 1955. In 1977 she received her Diploma di Licenza in Mathematics from Scuola Normale Superiore in Pisa. Since 2001 she is Associate Professor at the University of Pisa. Her areas of research are real and complex analytic geometry, real algebraic geometry, computational algebraic geometry.

Roberto Frigerio was born in Como in 1977. In 2005 he received his Ph.D. in Mathematics at Scuola Normale Superiore in Pisa. Since 2014 he is Associate Professor at the University of Pisa. His primary scientific interests are focused on low-dimensional topology, hyperbolic geometry and geometric group theory.

Rita Pardini was born in Lucca in 1960. She received her Ph.D. in Mathematics from Scuola Normale Superiore in Pisa in 1990; she is Full Professor at the University of Pisa since 2004. Her area of research is classical algebraic geometry, in particular algebraic surfaces and their moduli, irregular varieties and coverings.

Bibliographic information

  • Book Title Projective Geometry
  • Book Subtitle Solved Problems and Theory Review
  • Authors Elisabetta Fortuna
    Roberto Frigerio
    Rita Pardini
  • Series Title UNITEXT
  • Series Abbreviated Title UNITEXT
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-42823-9
  • eBook ISBN 978-3-319-42824-6
  • Series ISSN 2038-5714
  • Edition Number 1
  • Number of Pages XII, 266
  • Number of Illustrations 31 b/w illustrations, 0 illustrations in colour
  • Topics Projective Geometry
    Algebraic Geometry
  • Buy this book on publisher's site


“This is a modern textbook on classic projective geometry over (mostly) real and complex vectorspaces. … The book will also serve well as a source and reference for an undergraduate lecture plus exercise course on projective geometry.” (Hans-Peter Schröcker, zbMATH 1361.51004, 2017)