Enrico Arbarello, Maurizio Cornalba, Phillip Griffiths

Geometry of Algebraic Curves

Volume I
Mitwirkender: Arbarello, Enrico; Griffiths, Pillip A.; Cornalba, Maurizio

• Broschiertes Buch

Produktbeschreibung

In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

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Produktdetails

• Grundlehren der mathematischen Wissenschaften 267
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-2825-2
• Repr. d. Ausg. v. 1985
• Seitenzahl: 404
• Erscheinungstermin: 1. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 22mm
• Gewicht: 632g
• ISBN-13: 9781441928252
• ISBN-10: 1441928251
• Artikelnr.: 32210522

Inhaltsangabe

Preliminaries.- Determinantal Varieties.- to Special Divisors.- The Varieties of Special Linear Series on a Curve.- The Basic Results of the Brill-Noether Theory.- The Geometric Theory of Riemann's Theta Function.- The Existence and Connectedness Theorems for W d r (C).- Enumerative Geometry of Curves.

Rezensionen

From the reviews:

"This second volume will become the standard reference for researchers and students working on the algebraic geometry of curves. With almost 700 items in the rich 42-page bibliography, bibliographical notes at the end of every chapter to guide the reader and sets of (guided) exercises as in the first volume, this second volume is an interactive resource for everyone seriously interested on this beautiful part of algebraic geometry. We owe the authors a heartfelt thank you for writing such a rich, beautiful and full treatise."

(Felipe Zaldivar, The Mathematical Association of America, July, 2011)