Monografie Matematyczne

Projective Geometry and Formal Geometry

Authors: Badescu, Lucian Silvestru

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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.

Table of contents (14 chapters)

  • Extensions of Projective Varieties

    Bădescu, Lucian

    Pages 3-13

  • Proof of Theorem 1.3

    Bădescu, Lucian

    Pages 15-21

  • Counterexamples and Further Consequences

    Bădescu, Lucian

    Pages 23-30

  • The Zak Map of a Curve. Gaussian Maps

    Bădescu, Lucian

    Pages 31-38

  • Quasi-homogeneous Singularities and Projective Geometry

    Bădescu, Lucian

    Pages 39-48

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-7936-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-7643-7123-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-0348-9626-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Projective Geometry and Formal Geometry
Authors
Series Title
Monografie Matematyczne
Series Volume
65
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-7936-1
DOI
10.1007/978-3-0348-7936-1
Hardcover ISBN
978-3-7643-7123-4
Softcover ISBN
978-3-0348-9626-9
Series ISSN
0077-0507
Edition Number
1
Number of Pages
XIV, 214
Topics