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.

Autorentext

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.

Inhalt

1 Theory Review.- 2 Exercises on Projective Spaces.- 3 Exercises on Curves and Hypersurfaces.- 4 Exercises on Conics and Quadrics.