Moduli of Curves
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Moduli of Curves

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ISBN-13:
9780387984292
Einband:
Book
Erscheinungsdatum:
01.07.1998
Seiten:
388
Autor:
Joe Harris
Gewicht:
585 g
Format:
235x155x20 mm
Sprache:
Englisch
Beschreibung:
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. With over 180 exercises and 70 figures.
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.
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.

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