Gerd Fischer: Plane Algebraic Curves

Plane Algebraic Curves


Description

The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. In this book, Fischer looks at the classic entry point to the subject: plane algebraic curves. Here one quickly sees the mix of algebra and geometry, as well as analysis and topology, that is typical of complex algebraic geometry, but without the need for advanced techniques from commutative algebra or the abstract machinery of sheaves and schemes. In the first half of this book, Fischer introduces some elementary geometrical aspects, such as tangents, singularities, inflection points, and so on.The main technical tool is the concept of intersection multiplicity and Bezout's theorem. This part culminates in the beautiful Plucker formulas, which relate the various invariants introduced earlier. The second part of the book is essentially a detailed outline of modern methods of local analytic geometry in the context of complex curves. This provides the stronger tools needed for a good understanding of duality and an efficient means of computing intersection multiplicities introduced earlier.Thus, we meet rings of power series, germs of curves, and formal parametrizations. Finally, through the patching of the local information, a Riemann surface is associated to an algebraic curve, thus linking the algebra and the analysis.Concrete examples and figures are given throughout the text, and when possible, procedures are given for computing by using polynomials and power series. Several appendices gather supporting material from algebra and topology and expand on interesting geometric topics. This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help the student establish the appropriate geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher dimensional varieties. This is the English translation of a German work originally published by Vieweg Verlag (Wiesbaden, Germany).

In the New York Times bestseller that the Washington Post called "Lean In for misfits," Sophia Amoruso shares how she went from dumpster diving to founding one of the fastest-growing retailers in the world. In the summer of 1924, at a glittering society party held at the house, a young poet shot himself. The only witnesses were Hannah and Emmeline and only they -- and Grace -- know the Plane Algebraic Curves pdf truth. Star Wars Character Encyclopedia: Updated and Expanded, the definitive guide to the people, aliens, and droids of theStar Wars galaxy, is back, bigger and better than ever before, and packed with newStar Wars characters! A Book Blogger's Diary " Robin Kaye's Romeo, Romeo is sensational! I loved everything about this novel. The story, characters and writing are all five star material." Never has Inspector Montalbano's character -- a unique blend of humor, cynicism, compassion, earthiness, and love of good food -- been more compelling than in The Snack Thief. When an elderly man is stabbed to death in an elevator and a crewman on an Italian fishing trawler is machine-gunned by a Tunisian patrol boat off Sicily's coast, only Inspector Montalbano suspects a link between the two incidents. His investigation leads to the beautiful Karima, an impoverished house cleaner and sometime prostitute, whose young son steals other school children's mid-morning snacks. But Karima disappears, and the young snack thief's life -- as well as Montalbano's -- is endangered when the inspector exposes a viper's nest of government corruption and international intrigue.


____________________________
Author: Gerd Fischer
Number of Pages: 206 pages
Published Date: 01 Aug 2001
Publisher: American Mathematical Society
Publication Country: Providence, United States
Language: English
ISBN: 9780821821220
Download Link: Click Here
____________________________


Tags:

download pdf, for PC,download epub, free ebook, kindle, fb2,Plane Algebraic Curves kindle,rarepub download, download book, zip,download pdf Plane Algebraic Curves by Gerd Fischer for mac,facebook, book review, iOS, ebook pdf, paperback, iPad, download torrent, mobi, for mac, free pdf, download ebook, iPhone, Gerd Fischer free pdf,download pdf, ebook, pocket, Read online,

Ethics and Values in Social Work