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portada Geometry of Algebraic Curves: Volume i: 1 (Grundlehren der Mathematischen Wissenschaften)
Type
Physical Book
Publisher
Author
Year
1984
Language
English
Pages
387
Format
Hardcover
ISBN
0387909974
ISBN13
9780387909974
Edition No.
1
Categories

Geometry of Algebraic Curves: Volume i: 1 (Grundlehren der Mathematischen Wissenschaften)

Enrico Arbarello; Maurizio Cornalba; Phillip Griffiths; Joseph Daniel Harris (Author) · Springer · Hardcover

Geometry of Algebraic Curves: Volume i: 1 (Grundlehren der Mathematischen Wissenschaften) - Enrico Arbarello; Maurizio Cornalba; Phillip Griffiths; Joseph Daniel Harris

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Synopsis "Geometry of Algebraic Curves: Volume i: 1 (Grundlehren der Mathematischen Wissenschaften) "

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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