Elementary algebraic geometry
Author(s)
Bibliographic Information
Elementary algebraic geometry
(Graduate texts in mathematics, 44)
Springer-Verlag, c1977
- : us
- : gw
- : pbk
Available at / 97 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: usKEN||11||12481463
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Kobe University General Library / Library for Intercultural Studies
: us410-8-G4//44061000061118
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University of Toyama Library, Central Library図
: us414.5||K34||90076420,
: U.S.411.8||K34||El00083940 -
: U.S.414.6||5-3T20009441*,
: U.S.414.6||5T20007032*, : U.S.414.6||5-2T20009430* OPAC
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Hokkaido University, Faculty and Graduate School of Engineering図書
: U.S.dc19:516.35/k3413521120881
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science研究室
: us516/K3412020967608
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Note
Bibliography: p. 297
Includes index
Description and Table of Contents
- Volume
-
: us ISBN 9780387901992
Description
- Volume
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: pbk ISBN 9781461569015
Description
Table of Contents
- I Examples of curves.- 1 Introduction.- 2 The topology of a few specific plane curves.- 3 Intersecting curves.- 4 Curves over ?.- II Plane curves.- 1 Projective spaces.- 2 Affine and projective varieties
- examples.- 3 Implicit mapping theorems.- 4 Some local structure of plane curves.- 5 Sphere coverings.- 6 The dimension theorem for plane curves.- 7 A Jacobian criterion for nonsingularity.- 8 Curves in ?2(?) are connected.- 9 Algebraic curves are orientable.- 10 The genus formula for nonsingular curves.- III Commutative ring theory and algebraic geometry.- 1 Introduction.- 2 Some basic lattice-theoretic properties of varieties and ideals.- 3 The Hilbert basis theorem.- 4 Some basic decomposition theorems on ideals and varieties.- 5 The Nullstellensatz: Statement and consequences.- 6 Proof of the Nullstellensatz.- 7 Quotient rings and subvarieties.- 8 Isomorphic coordinate rings and varieties.- 9 Induced lattice properties of coordinate ring surjections
- examples.- 10 Induced lattice properties of coordinate ring injections.- 11 Geometry of coordinate ring extensions.- IV Varieties of arbitrary dimension.- 1 Introduction.- 2 Dimension of arbitrary varieties.- 3 The dimension theorem.- 4 A Jacobian criterion for nonsingularity.- 5 Connectedness and orientability.- 6 Multiplicity.- 7 Bezout's theorem.- V Some elementary mathematics on curves.- 1 Introduction.- 2 Valuation rings.- 3 Local rings.- 4 A ring-theoretic characterization of nonsingularity.- 5 Ideal theory on a nonsingular curve.- 6 Some elementary function theory on a nonsingular curve.- 7 The Riemann-Roch theorem.- Notation index.
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