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Titlebook: Geometry of Algebraic Curves; Volume I E. Arbarello,M. Cornalba,J. Harris Textbook 1985 Springer-Verlag New York 1985 Algebraic.Curves.Geom

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书目名称Geometry of Algebraic Curves
副标题Volume I
编辑E. Arbarello,M. Cornalba,J. Harris
视频video
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Geometry of Algebraic Curves; Volume I E. Arbarello,M. Cornalba,J. Harris Textbook 1985 Springer-Verlag New York 1985 Algebraic.Curves.Geom
描述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 se
出版日期Textbook 1985
关键词Algebraic; Curves; Geometry; algebra; moduli space
版次1
doihttps://doi.org/10.1007/978-1-4757-5323-3
isbn_softcover978-1-4419-2825-2
isbn_ebook978-1-4757-5323-3Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag New York 1985
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0072-7830 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 se978-1-4419-2825-2978-1-4757-5323-3Series ISSN 0072-7830 Series E-ISSN 2196-9701
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Methodologie des Rechtsstudiums,merative problems that arise in the theory of curves and linear systems. While this is in some sense a quantitative approach, qualitative results may also emerge. For example, the answer to the enumerative question: “How many ..’s does a curve . possess” (Theorem (4.4) in Chapter VII) implies the existence theorem (Theorem (2.3) in Chapter VII).
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Determinantal Varieties,f the results in this chapter will be to the varieties of special divisors on curves. These varieties have in fact a natural determinantal structure defined in terms of the Brill-Noether matrix, and their study is the central theme of this book. Another ubiquitous example of determinantal variety is the one of rational normal scrolls.
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Geometry of Algebraic Curves978-1-4757-5323-3Series ISSN 0072-7830 Series E-ISSN 2196-9701
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