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Geometry of Algebraic Curves: Volume I

Geometry of Algebraic Curves: Volume I
Catalogue Information
Field name Details
Dewey Class 516.35
Title Geometry of Algebraic Curves ([EBook]) : Volume I / by E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris.
Author Arbarello, Enrico
Added Personal Name Cornalba, M.
Griffiths, P. A.
Harris, J.
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 1985.
Physical Details XVI, 387 pages : online resource.
Series Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 267
ISBN 9781475753233
Summary Note 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).:
Contents note 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.
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