Moduli of Curves (Graduate Texts in Mathematics, 187)

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.

Science & Math

Joe Harris,Ian Morrison

Mathematics

Springer

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Books by Joe Harris,Ian Morrison

See the best price to sell, buy, or rent books by Joe Harris,Ian Morrison. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Moduli of Curves (Graduate Texts in Mathematics, 187)