eBook ISBN:  9781470424046 
Product Code:  CBMS/44.E 
List Price:  $23.00 
Individual Price:  $18.40 
eBook ISBN:  9781470424046 
Product Code:  CBMS/44.E 
List Price:  $23.00 
Individual Price:  $18.40 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 44; 1980; 25 ppMSC: Primary 14; Secondary 32
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 RiemannRoch 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 (a) the RiemannRoch theorem, (b) Clifford's theorem and the \(\mu_0\)mapping, and (c) canonical curves and the BrillNoether 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 (a) Abel's theorem, (b) the reappearance of the BrillNoether matrix with applications to the singularities of \(W_d\) and the KleimanLaksov existence proof, (c) special linear systems in low genus.
Readership 
Table of Contents

Chapters

Preface

Part 1. The RiemannRoch theorem and special divisors

Part 2. The Jacobian variety and special divisors


Reviews

All discussion, as easy and elementary as possible, is a successful attempt to give an introduction to an advanced theory, that could also be followed by a reader even only superficially familiar with Riemann surfaces.
Ciro Ciliberto, Mathematical Reviews


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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 RiemannRoch 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 (a) the RiemannRoch theorem, (b) Clifford's theorem and the \(\mu_0\)mapping, and (c) canonical curves and the BrillNoether 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 (a) Abel's theorem, (b) the reappearance of the BrillNoether matrix with applications to the singularities of \(W_d\) and the KleimanLaksov existence proof, (c) special linear systems in low genus.

Chapters

Preface

Part 1. The RiemannRoch theorem and special divisors

Part 2. The Jacobian variety and special divisors

All discussion, as easy and elementary as possible, is a successful attempt to give an introduction to an advanced theory, that could also be followed by a reader even only superficially familiar with Riemann surfaces.
Ciro Ciliberto, Mathematical Reviews