Algebraic Functions and Projective Curves

David Goldschmidt

ISBN 10: 0387954325 / ISBN 13: 9780387954325

Editore: Springer New York, Springer US Okt 2002, 2002

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Neuware -This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University. The motivation was to try to understand the basic facts about algebraic curves without the modern prerequisite machinery of algebraic geometry. Of course, one might well ask if this is a good thing to do. There is no clear answer to this question. In short, we are trading off easier access to the facts against a loss of generality and an impaired understanding of some fundamental ideas. Whether or not this is a useful tradeoff is something you will have to decide for yourself. One of my objectives was to make the exposition as self-contained as possible. Given the choice between a reference and a proof, I usually chose the latter. - though I worked out many of these arguments myself, I think I can con dently predict that few, if any, of them are novel. I also made an effort to cover some topics that seem to have been somewhat neglected in the expository literature.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 204 pp. Englisch.

Codice articolo 9780387954325

Dati bibliografici

• Titolo: Algebraic Functions and Projective Curves
• Editore: Springer New York, Springer US Okt 2002
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 0387954325
• ISBN 13: 9780387954325
• Rilegatura: Buch
• Condizione: Neu

Descrizione articolo

Riassunto

This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves.

Dalla quarta di copertina

This book provides a self-contained exposition of the theory of algebraic curves without requiring any of the prerequisites of modern algebraic geometry. The self-contained treatment makes this important and mathematically central subject accessible to non-specialists. At the same time, specialists in the field may be interested to discover several unusual topics. Among these are Tates theory of residues, higher derivatives and Weierstrass points in characteristic p, the Stöhr--Voloch proof of the Riemann hypothesis, and a treatment of inseparable residue field extensions. Although the exposition is based on the theory of function fields in one variable, the book is unusual in that it also covers projective curves, including singularities and a section on plane curves.
David Goldschmidt has served as the Director of the Center for Communications Research since 1991. Prior to that he was Professor of Mathematics at the University of California, Berkeley.