# Plane Algebraic Curves

#### ISBN: 3764317698

#### Category: Uncategorized

Posted on 2007-11-01, updated at 2008-11-22. By anonymous.

Description

**Egbert Brieskorn, Horst Knorrer, â€œPlane Algebraic Curvesâ€**

Publisher: Birkhauser | Pages: 730 | ISBN : 3764317698 | DjVu | 6.2 Mb

Chapter 1 is a very exciting tour of algebraic curves through history with lots of examples and pictures. There is a wealth of examples already from Greek days. The two main systematising tools are analytic geometry (chapter 2) and projective geometry (chapter 3). Analytic geometry imposes a hierarchy on algebraic curves according to the degree of their equation. The pivotal case is the cubics. Newton carried out an algebraic classification of cubics into 72 cases, but he also noted that any cubic could be obtained from one of only five standard cases by central projection. A real theory of projective geometry, however, would have to wait until the 19th century and the realisation that the complex projective plane, realised by homogenous coordinates, is the proper setting for this theory. Thus we now have a clear algebraic basis for our theory so we now leave the historical perspective and start to develop the theory more systematically (chapters 4-6). With the basic machinery of polynomial algebra we can now treat properly some concepts we had seen in special cases (reducibility of curves, singular points) and some theorems we had only felt (BÃ©zout's theorem, point-line duality). (Already here the authors sneak in some non-standard material (singularities as torus knots, topological proof of BÃ©zout's theorem) to harmonise with the more modern theory later in the book.) In chapter 7 we see applications, in particular the showcase theorem on the configuration of the inflections points of a cubic, and the role of cubics elsewhere in mathematics (the addition-of-points operation makes them abelian manifolds and they are also the tori on which elliptic functions live). These were the nonsingular cubics. Now we shall study curves with singularities. This is an opportunity to include decidedly more modern work, and our authors get carried away in an enormous 250-page chapter 8 on the resolution of singularities. But in chapter 9 it's back to the classics, namely the basic formulae on global invariants. First the PlÃ¼cker formulae. For a nonsingular curve of order n, the order of its dual curve is n(n-1) and the number of inflection points is 3n(n-2). When the curve has singularities one must add correction terms. PlÃ¼cker found the correct formulae when the singularities are not worse than ordinary double points and simple cusps. Weierstrass and M. Noether generalised. Similarly for the genus of a curve. For nonsingular curves it's (n-1)(n-2)/2; Clebsch found the formula for when there are only easy singularities; M. Noether generalised. As Riemann knew, the genus is also the number of linearly independent integrals of the first kind, and we spend the last 70 pages expanding this function theoretic point of view.

MIRROR: IceFile.com

MIRROR: IceFile.com

**DOWNLOAD Plane Algebraic Curves:**http://depositfiles.com/files/2226005

**DOWNLOAD Plane Algebraic Curves:**http://depositfiles.com/files/2226005

**DOWNLOAD Plane Algebraic Curves:**http://depositfiles.com/files/2226005

**Mirror: http://w14.easy-share.com/8889991.html**

Sponsored High Speed Downloads

6508 dl's @ 3597 KB/s

**Download Now**[Full Version]

7540 dl's @ 2722 KB/s

**Download Link 1**- Fast Download

6123 dl's @ 2112 KB/s

**Download Mirror**- Direct Download

Search More...

**Plane Algebraic Curves**

Related Archive Books

**Archive Books related to "Plane Algebraic Curves":**

- 2011-06-23Plane Algebraic Curves
- 2011-06-20Plane Algebraic Curves

Links

Download this book

No active download links here?

Please check the description for download links if any or do a search to find alternative books.Related Books

- Ebooks list page : 1391
- 2018-12-06Introduction to
*Plane Algebraic Curves* - 2018-01-06[PDF] A Guide to
*Plane Algebraic Curves*(Dolciani Mathematical Expositions) - 2018-01-04[PDF]
*Plane Algebraic Curves*(Student Mathematical Library, V. 15) - 2017-11-15[PDF]
*Plane Algebraic Curves*(Birkhauser, 1986) - 2014-04-27
*Plane Algebraic Curves*: Translated by John Stillwell (repost) -*Removed* - 2014-02-04
*Plane Algebraic Curves*(Student Mathematical Library, V. 15) (Repost) - 2013-12-31A Guide to
*Plane Algebraic Curves* - 2013-11-11
*Plane Algebraic Curves*(Student Mathematical Library, V. 15) - 2013-05-18
*Plane Algebraic Curves*(repost) - 2013-03-05
*Plane Algebraic Curves*: Translated by John Stillwell - 2012-02-24Introduction to
*Plane Algebraic Curves*(Repost) - 2011-06-23
*Plane Algebraic Curves* - 2011-06-20
*Plane Algebraic Curves* - 2011-03-26
*Plane Algebraic Curves*by Egbert Brieskorn (Repost) - 2010-01-02Introduction to
*Plane Algebraic Curves*(repost) - 2007-12-07Introduction to
*Plane Algebraic Curves* - 2007-12-01Introduction to
*Plane Algebraic Curves* - 2019-12-23Pencils of Cubics and
*Algebraic Curves*in the Real Projective*Plane*-*Removed* - 2020-11-29Elementary Geometry of
*Algebraic Curves*

Comments

**No comments for "Plane Algebraic Curves"**.

Add Your Comments

- Download links and password may be in the description section, read description carefully!
- Do a search to find mirrors if no download links or dead links.