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Titlebook: Algebraic Surfaces; Oscar Zariski Book 1995Latest edition Springer-Verlag Berlin Heidelberg 1995 Dimension.Excel.algebra.algebraic curve.a

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期刊全称Algebraic Surfaces
影响因子2023Oscar Zariski
视频video
学科分类Classics in Mathematics
图书封面Titlebook: Algebraic Surfaces;  Oscar Zariski Book 1995Latest edition Springer-Verlag Berlin Heidelberg 1995 Dimension.Excel.algebra.algebraic curve.a
影响因子The aim of the present monograph is to give a systematic exposition of the theory of algebraic surfaces emphasizing the interrelations between the various aspects of the theory: algebro-geometric, topological and transcendental. To achieve this aim, and still remain inside the limits of the allotted space, it was necessary to confine the exposition to topics which are absolutely fundamental. The present work therefore makes no claim to completeness, but it does, however, cover most of the central points of the theory. A presentation of the theory of surfaces, to be effective at all, must above all give the typical methods of proof used in the theory and their underlying ideas. It is especially true of algebraic geometry that in this domain the methods employed are at least as important as the results. The author has therefore avoided, as much as possible, purely formal accounts of results. The proofs given are of necessity condensed, for reasons of space, but no attempt has been made to condense them beyond the point of intelligibility. In many instances, due to exigencies of simplicity and rigor, the proofs given in the text differ, to a greater or less extent, from the proofs giv
Pindex Book 1995Latest edition
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Continuous Non-linear Systems,surfaces carrying an irrational pencil Σ of curves. Obviously, such a pencil (supposing for simplicity that the curves of the pencil are irreducible) cannot be contained in a linear system of dimension ., where . is necessarily ≧2, because the curves of the pencil are of virtual degree zero (II, 1).
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Magmatic and Sub-magmatic Deformation,. is any 1-cycle on ., the integral . is called . if . ≁ 0 on ., a . if . ∽ 0. A simple integral . without periods (i. e. whose periods all vanish) is a constant, a rational function or a logarithmo-rational function of ., according as . is of the first, second or third kind.
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Simple and Double Integrals on an Algebraic Surface,. is any 1-cycle on ., the integral . is called . if . ≁ 0 on ., a . if . ∽ 0. A simple integral . without periods (i. e. whose periods all vanish) is a constant, a rational function or a logarithmo-rational function of ., according as . is of the first, second or third kind.
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https://doi.org/10.1007/0-306-47543-Xnch point of . if . is fixed and generic. It may be necessary to include the line at infinity of the projective plane (.) in the branch curve. However, we may always choose the coördinates . and . in such a manner that the line at infinity does not belong to the branch curve.
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