# Moduli of Curves / Edition 1

ISBN-10: 0387984291

ISBN-13: 9780387984292

Pub. Date: 07/01/1998

Publisher: Springer New York

A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric

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## Overview

A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the 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, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys 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.

## Product Details

ISBN-13:
9780387984292
Publisher:
Springer New York
Publication date:
07/01/1998
Series:
Graduate Texts in Mathematics Series, #187
Edition description:
1998
Pages:
369
Product dimensions:
0.80(w) x 6.14(h) x 9.21(d)

## Related Subjects

Parameter spaces: Constructions and examples.- Basic facts about moduli spaces of curves.- Techniques.- Construction of $$\overline M _g$$ .- Limit Linear Series and Brill-Noether theory.- Geometry of moduli spaces: Selected results.

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