ENGLISH

Algebraic curves and Riemann surfaces

By Rick Miranda

Book information

Publisher
American Mathematical Society
Year
1995
ISBN
0821802682, 9780821802687
ISSN
1065-7339
LCC
QA565 .M687 1995
Open Library ID
OL1270748M
Language
english
Format
DJVU
Filesize
4 MB (4182439 bytes)
Series
Graduate studies in mathematics 5
Pages
399\399
Topic
Mathematics Algebra
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

This text is an introduction to the theory of algebraic curves defined over the complex numbers. It begins with the definitions and first properties of Riemann surfaces, with special attention paid to the Riemann sphere, complex tori, hyperelliptic curves, smooth plane curves, and projective curves. The heart of the book is the treatment of divisors and rational functions, culminating in the theorems of Riemann-Roch and Abel and the analysis of the canonical map. Sheaves, cohomology, the Zariski topology, line bundles, and the Picard group are developed after these main theorems are proved and applied, as a bridge from the classical material to the modern language of algebraic geometry.

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