✦ LIBER ✦

Algebraic curves and Riemann surfaces

✍ Scribed by Rick Miranda

Book ID: 127418086
Publisher: American Mathematical Society
Year: 1995
Tongue: English
Weight: 4 MB
Series: Graduate studies in mathematics 5
Category: Library
City: Providence, R.I
ISBN-13: 9780821802687
ISSN: 1065-7339

No coin nor oath required. For personal study only.

✦ Synopsis

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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