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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Geometry of Algebraic Curves - Volume I (Paperback, 1985 ed.)
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Geometry of Algebraic Curves - Volume I (Paperback, 1985 ed.)
Series: Grundlehren der mathematischen Wissenschaften, 267
Expected to ship within 10 - 15 working days
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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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