By Phillip A. Griffiths
Algebraic curves and compact Riemann surfaces contain the main built and arguably the main attractive component of algebraic geometry. even though, the vast majority of books written at the topic talk about algebraic curves and compact Riemann surfaces individually, as components of distinctive common theories. so much texts and collage classes on curve concept regularly finish with the Riemann-Roch theorem, although this theorem is the gateway to a few of the main interesting ends up in the idea of algebraic curves. This booklet relies on a six-week sequence of lectures awarded via the writer to 3rd- and fourth-year undergraduates and graduate scholars at Beijing college in 1982. The lectures started with minimum technical necessities (a operating wisdom of undemanding advanced functionality idea and algebra including a few publicity to topology of compact surfaces) and proceeded on to the Riemann-Roch and Abel theorems. This publication differs from a couple of contemporary books in this topic in that it combines analytic and geometric equipment on the outset, in order that the reader can clutch the fundamental result of the topic. even supposing such glossy suggestions of sheaf conception, cohomology, and commutative algebra should not lined right here, the e-book presents an outstanding starting place to continue to extra complicated texts as a rule algebraic geometry, advanced manifolds, and Riemann surfaces, in addition to algebraic curves. Containing a number of routines and assessments, this e-book might make a very good introductory textual content.
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