Moduli of Curves

Joe Harris, Ian Morrison (Autoren)

Buch | Hardcover

369 Seiten

1998 | 1998 ed.
Springer-Verlag New York Inc.
978-0-387-98438-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	1.7.1998
Reihe/Serie	Graduate Texts in Mathematics ; 187
Zusatzinfo	6 Tables, black and white; XIII, 369 p.
Verlagsort	New York, NY
Sprache	englisch
Gewicht	680 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-387-98438-0 / 0387984380
ISBN-13	978-0-387-98438-4 / 9780387984384
Zustand	Neuware