# Moduli of Curves

• Joe Harris
• Ian Morrison
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 187)

1. Front Matter
Pages i-xiii
2. Pages 35-80
3. Pages 81-190
4. Pages 191-239
5. Pages 240-285
6. Pages 286-343
7. Back Matter
Pages 345-369

### Introduction

Aims Theaimofthisbookistoprovideaguidetoarichandfascinatings- ject: algebraic curves, and how they vary in families. The revolution that the ?eld of algebraic geometry has undergone with the introd- tion of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understandthebehaviorofcurvesinwaysthatsimplywerenotpos- ble a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving long-standing problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn’t intended to be a de?nitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to - cus on examples and applications rather than on foundations. When discussing techniques we’ve chosen to sacri?ce proofs of some, even basic,results—particularlywherewecanprovideagoodreference— inordertoshowhowthemethodsareusedtostudymoduliofcurves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication.

### Keywords

Dimension Divisor Grad algebraic curve algebraic geometry deformation theory

#### Authors and affiliations

• Joe Harris
• 1
• Ian Morrison
• 2
1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
2. 2.Department of MathematicsFordham UniversityBronxUSA

### Bibliographic information

• DOI https://doi.org/10.1007/b98867
• Copyright Information Springer-Verlag New York, Inc. 1998
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-98438-4
• Online ISBN 978-0-387-22737-5
• Series Print ISSN 0072-5285
• Buy this book on publisher's site