An Introduction to the Theory of Special Divisors on Algebraic Curves (Cbms Regional Conference Series in Mathematics)

Phillip Griffiths

ISBN 10: 0821816942 / ISBN 13: 9780821816943

Published by Amer Mathematical Society, 1980

About this Item

Former library book; May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less 0.15.

Seller Inventory # G0821816942I4N10

Bibliographic Details

• Title: An Introduction to the Theory of Special Divisors on Algebraic Curves (Cbms Regional Conference Series in Mathematics)
• Publisher: Amer Mathematical Society
• Publication Date: 1980
• Language: English
• ISBN 10: 0821816942
• ISBN 13: 9780821816943
• Binding: Paperback
• Condition: Very Good
• Dust Jacket Condition: No Jacket
• Weight: 0.15 pounds

About this title

Synopsis

In May, 1979, an NSF Regional Conference was held at the University of Georgia in Athens. The topic of the conference was 'Special divisors on algebraic curves'. This monograph gives an exposition of the elementary aspects of the theory of special divisors together with an explanation of some more advanced results that are not too technical. As such, it is intended to be an introduction to recent sources. As with most subjects, one may approach the theory of special divisors from several points of view. The one adopted here pertains to Clifford's theorem, and may be informally stated as follows: The failure of a maximally strong version of Clifford's theorem to hold imposes nontrivial conditions on the moduli of an algebraic curve.This monograph contains two sections, respectively studying special divisors using the Riemann-Roch theorem and the Jacobian variety. In the first section the author begins pretty much at ground zero, so that a reader who has only passing familiarity with Riemann surfaces or algebraic curves may be able to follow the discussion. The respective subtopics in this first section are the Riemann-Roch theorem, Clifford's theorem and the $\mu_0$-mapping, and canonical curves and the Brill-Noether matrix. In the second section he assumes a little more, although again an attempt has been made to explain, if not prove, anything. The respective subtopics are Abel's theorem, the reappearance of the Brill-Noether matrix with applications to the singularities of $W_d$ and the Kleiman-Laksov existence proof, and special linear systems in low genus.