Advanced Lectures in Mathematics

Ruled Varieties

An Introduction to Algebraic Differential Geometry

Authors: Fischer, Gerd, Piontkowski, Jens

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-322-80217-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-528-03138-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable.

This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties.

Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course.

About the authors

Prof. Dr. em. Gerd Fischer war viele Jahre Professor für Mathematik an der Universität Düsseldorf. Er ist jetzt Gastprofessor an der Fakultät für Mathematik der TU München. Gerd Fischer ist Autor zahlreicher erfolgreicher Lehrbücher, u.a. der Linearen Algebra (vieweg studium - Grundkurs Mathematik).
Dr. Jens Piontkowski ist Hochschuldozent am Mathematischen Institut der Heinrich-Heine-Universität Düsseldorf.

Table of contents (4 chapters)

  • Review from Classical Differential and Projective Geometry

    Fischer, Gerd (et al.)

    Pages 1-11

  • Grassmannians

    Fischer, Gerd (et al.)

    Pages 12-48

  • Ruled Varieties

    Fischer, Gerd (et al.)

    Pages 49-118

  • Tangent and Secant Varieties

    Fischer, Gerd (et al.)

    Pages 119-136

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-322-80217-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-528-03138-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Ruled Varieties
Book Subtitle
An Introduction to Algebraic Differential Geometry
Authors
Series Title
Advanced Lectures in Mathematics
Copyright
2001
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
eBook ISBN
978-3-322-80217-0
DOI
10.1007/978-3-322-80217-0
Softcover ISBN
978-3-528-03138-1
Series ISSN
0932-7134
Edition Number
1
Number of Pages
X, 142
Topics