ENGLISH

Moduli of Curves

By Joe Harris , Ian Morrison

Book information

Publisher
Springer
Year
1998
ISBN
0387984380, 9780387984384, 9780387227375, 0387984291
LCC
QA564 .H244 1998
Open Library ID
OL20748927M
Language
english
Format
PDF
Filesize
2 MB (1870853 bytes)
Series
Graduate tests in mathematics 187
Edition
1
Pages
381\381
Topic
Mathematics Algebra
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

This book provides a guide to a rich and fascinating subject: algebraic curves and how they vary in families. The aim has been to provide a broad but compact overview of the field, which will be accessible to readers with a modest background in algebraic geometry. Many techniques including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory are developed, with a focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, to illustrate typical applications with the proofs of the Brill-Noether and Gieseker -Petri theorems via limit linear series, and to survey the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results! and open problems about important topics which are not covered in detail.

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