Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Projective Geometry and Formal Geometry

Projective Geometry and Formal Geometry

Series: Monografie Matematyczne, Vol. 65

Badescu, Lucian Silvestru

2004, XIV, 214 p.

A product of Birkhäuser Basel
Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$99.00

(net) price for USA

ISBN 978-3-0348-7936-1

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$139.00

(net) price for USA

ISBN 978-3-7643-7123-4

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$129.00

(net) price for USA

ISBN 978-3-0348-9626-9

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • About this book

The aim of this monograph is to introduce the reader to modern methods of projective geometry involving certain techniques of formal geometry. Some of these methods are illustrated in the first part through the proofs of a number of results of a rather classical flavor, involving in a crucial way the first infinitesimal neighbourhood of a given subvariety in an ambient variety. Motivated by the first part, in the second formal functions on the formal completion X/Y of X along a closed subvariety Y are studied, particularly the extension problem of formal functions to rational functions.
The formal scheme X/Y, introduced to algebraic geometry by Zariski and Grothendieck in the 1950s, is an analogue of the concept of a tubular neighbourhood of a submanifold of a complex manifold. It is very well suited to study the given embedding Y\subset X. The deep relationship of formal geometry with the most important connectivity theorems in algebraic geometry, or with complex geometry, is also studied. Some of the formal methods are illustrated and applied to homogeneous spaces.
The book contains a lot of results obtained over the last thirty years, many of which never appeared in a monograph or textbook. It addresses to algebraic geometers as well as to those interested in using methods of algebraic geometry.

Content Level » Research

Keywords » Algebraic geometry - Complex analysis - Formal geometry - Homogenous spaces - Meromorphic function - Projective geometry - Projective varieties - manifold

Related subjects » Birkhäuser Mathematics

Table of contents 

I Special Chapters of Projective Geometry.- 1 Extensions of Projective Varieties.- 2 Proof of Theorem 1.3.- 3 Counterexamples and Further Consequences.- A Counterexample in Characteristic 2.- A Counterexample in Characteristic 2.- 4 The Zak Map of a Curve. Gaussian Maps.- General Gaussian Maps.- Properties.- Gaussian Maps of Polarized Curves.- 5 Quasi-homogeneous Singularities and Projective Geometry.- 6 A Characterization of Linear Subspaces.- 7 Cohomological Dimension and Connectedness Theorems.- Cohomological Dimension.- Weighted Projective Spaces.- Connectedness Theorem.- 8 A Problem of Complete Intersection.- Appendix A.- Appendix B.- II Formal Functions in Algebraic Geometry.- 9 Basic Definitions and Results.- 10 Lefschetz Theory and Meromorphic Functions.- Grothendieck—Lefschetz Conditions.- Formal and Meromorphic Functions.- 11 Connectedness and Formal Functions.- 12 Further Results on Formal Functions.- Appendix C.- 13 Formal Functions on Homogeneous Spaces.- Appendix D.- 14 Quasi-lines on Projective Manifolds.- Glossary of Notation.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Algebraic Geometry.

Additional information