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OverviewA 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. Full Product DetailsAuthor: Joe Harris , Ian MorrisonPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1998 ed. Volume: 187 Weight: 0.680kg ISBN: 9780387984384ISBN 10: 0387984380 Pages: 369 Publication Date: 01 July 1998 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Out of Print Availability: Out of stock  Table of ContentsParameter 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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