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Moduli of Curves (Graduate Texts in Mathematics)

Posted on 2010-04-10




Name:Moduli of Curves (Graduate Texts in Mathematics)
ASIN/ISBN:0387984380
Language:English
File size:2.3 Mb
Publish Date: 1998-07-01
ISBN: 0387984380
File Type: PDF
Pages: 366 pages
File Size: 2,3 Mb
Other Info: Springer
   Moduli of Curves (Graduate Texts in Mathematics)

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Roberta B. Carey, Mindy G. Schuster, Karin L. McGowan "

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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