Overview

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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9781280010293

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