Moduli of Curves
(Sprache: Englisch)
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...
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Klappentext zu „Moduli of Curves “
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.
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
Inhaltsverzeichnis zu „Moduli of Curves “
I Parameter spaces: constructions and examples II Basic facts about moduli spaces of curves
III Techniques
IV Construction of M_g
V Limit Linear Series and the Brill-Noether Theory
VI Geometry of moduli spaces: Selected Results
Bibliographische Angaben
- Autoren: Joe Harris , Ian Morrison
- 1998, 369 Seiten, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, New York
- ISBN-10: 0387984291
- ISBN-13: 9780387984292
- Erscheinungsdatum: 01.07.1998
Sprache:
Englisch
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