Moduli of Curves

Ian Morrison

ISBN 10: 0387984291 / ISBN 13: 9780387984292

Editore: Springer New York, Springer US Jul 1998, 1998

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Neuware -The aim of this book is to provide a guide to a rich and fascinating subject: algebraic curves, and how they vary in families. The revolution that the field of algebraic geometry has undergone with the introduction of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understand the behavior of curves in ways that simply were not possible a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving longstanding problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn¿t intended to be a definitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to focus on examples and applications rather than on foundations. When discussing techniqueswe¿ve chosen to sacrifice proofs of some, even basic,results¿particularly where we can provide a good reference¿ in order to show how the methods are used to study moduli of curves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication. 388 pp. Englisch.

Codice articolo 9780387984292

Dati bibliografici

• Titolo: Moduli of Curves
• Editore: Springer New York, Springer US Jul 1998
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0387984291
• ISBN 13: 9780387984292
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 21 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 21 millimetri di profondità
• Peso: 587 grammi

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Riassunto

The aim of this book is to provide a guide to a rich and fascinating subject: algebraic curves, and how they vary in families. The revolution that the field of algebraic geometry has undergone with the introduction of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understand the behavior of curves in ways that simply were not possible a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving longstanding problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn’t intended to be a definitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to focus on examples and applications rather than on foundations. When discussing techniqueswe’ve chosen to sacrifice proofs of some, even basic,results―particularly where we can provide a good reference― in order to show how the methods are used to study moduli of curves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication.

Contenuti

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.