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1.

図書

図書
Carlos Andradas, Ludwig Bröcker, Jesús M. Ruiz
出版情報: Berlin ; Tokyo : Springer-Verlag, c1996  ix, 270 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 33
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2.

図書

図書
by W.V.D. Hodge and D. Pedoe
出版情報: Cambridge : Cambridge University Press, 1994  3 v. ; 23 cm
シリーズ名: Cambridge mathematical library
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目次情報: 続きを見る
Book 5: Birational Geometry / Part I:
Ideal theory of commutative rings / 15:
The arithmetic theory of varieties / 16:
Valuation theory / 17:
Birational transformations / 18:
Book 5: Birational Geometry / Part I:
Ideal theory of commutative rings / 15:
The arithmetic theory of varieties / 16:
3.

図書

図書
by Shreeram Abhyankar
出版情報: Princeton, N.J. : Princeton University Press, 1959  vi, 96 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 43
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Preface
Introduction
General Ramification Theory / I:
Elementary lemmas from ideal theory / 1:
Primary decomposition in non-noetherian rings / 2:
Integral dependence / 3:
Linear algebra / 4:
Discriminant of an algebra / 5:
The discriminant ideal / 6:
Galois theory of local rings / 7:
Valuation Theory / II:
Ordered abelian groups / 8:
Valuations / 9:
Specialization and composition of valuations / 10:
Ramification theory of valuations / 11:
Valuations of algebraic function fields / 12:
Noetherian Local Rings / III:
The dimension of a noetherian local ring / 13:
Quadratic transforms / 14:
Two-Dimensional Local Domains / IV:
Limits of quadratic sequences / 15:
Uniformization in a two-dimensional regular local domain / 16:
Uniformization for a two-dimensional algebraic function field / 17:
Varieties and Transformations / V:
Projective varieties / 18:
Resolution of singularities of algebraic surfaces / 19:
Bibliography
Preface
Introduction
General Ramification Theory / I:
4.

図書

図書
by V.P. Kompaniec ... [et al.]
出版情報: Providence, R.I. : American Mathematical Society, 1968  iv, 260 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 73
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5.

図書

図書
Monique Hakim
出版情報: Berlin ; Heidelberg ; New York : Springer-Verlag, 1972  vi, 158 p. ; 23 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 64
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6.

図書

図書
by W.V.D. Hodge and D. Pedoe
出版情報: Cambridge : Cambridge University Press, 1947-1954  3 v. ; 23 cm
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7.

図書

図書
Jacek Bochnak, Michel Coste, Marie-Françoise Roy
出版情報: Berlin : Springer, c1998  ix, 430 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 36
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8.

図書

図書
F. Hirzebruch
出版情報: Berlin ; New York : Springer-Verlag, 1966  ix, 232 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 131
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9.

図書

図書
[par] A. Grothendieck [et] J.A. Dieudonné
出版情報: Berlin ; New York : Springer-Verlag, 1971  ix, 466 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 166
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10.

図書

図書
I.R. Shafarevich ; translated from the Russian by K.A. Hirsch
出版情報: Berlin ; New York : Springer-Verlag, 1974  xv, 439 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 213
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11.

図書

図書
Eberhard Freitag, Reinhardt Kiehl ; with an historical introduction by J.A. Dieudonné
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  xviii, 317 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 13
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12.

図書

図書
Tadao Oda
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  viii, 212 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 15
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13.

図書

図書
David A. Cox, Sheldon Katz
出版情報: Providence, R.I. : American Mathematical Society, c1999  xxi, 469 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 68
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目次情報: 続きを見る
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
14.

図書

図書
Serge Lang
出版情報: New York : Interscience Publishers, c1962  x, 170 p. ; 24 cm
シリーズ名: Interscience tracts in pure and applied mathematics ; no. 11
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15.

図書

図書
Joe Harris
出版情報: New York ; Tokyo : Springer-Verlag, c1992  xix, 328 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 133
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Preface
Acknowledgments
Using This Book
Examples of Varieties and Maps / Part I:
Affine and Projective Varieties / Lecture 1:
A Note About Our Field
Affine Space and Affine Varieties
Projective Space and Projective Varieties
Linear Spaces
Finite Sets
Hypersurfaces
Analytic Subvarieties and Submanifolds
The Twisted Cubic
Rational Normal Curves
Determinantal Representation of the Rational Normal Curve
Another Parametrization of the Rational Normal Curve
The Family of Plane Conics
A Synthetic Construction of the Rational Normal Curve
Other Rational Curves
Varieties Defined over Subfields of K
A Note on Dimension, Smoothness, and Degree
Regular Functions and Maps / Lecture 2:
The Zariski Topology
Regular Functions on an Affine Variety
Projective Varieties
Regular Maps
The Veronese Map
Determinantal Representation of Veronese Varieties
Subvarieties of Veronese Varieties
The Segre Maps
Subvarieties of Segre Varieties
Products of Varieties
Graphs
Fiber Products
Combinations of Veronese and Segre Maps
Cones, Projections, and More About Products / Lecture 3:
Cones
Quadrics
Projections
More Cones
More Projections
Constructible Sets
Families and Parameter Spaces / Lecture 4:
Families of Varieties
The Universal Hyperplane
The Universal Hyperplane Section
Parameter Spaces of Hypersurfaces
Universal Families of Hypersurfaces
A Family of Lines
Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz / Lecture 5:
Generating Ideals
Ideals of Projective Varieties
Irreducible Varieties and Irreducible Decomposition
General Objects
General Projections
General Twisted Cubics
Double Point Loci
A Little Algebra
Restatements and Corollaries
Grassmannians and Related Varieties / Lecture 6:
Grassmannians
Subvarieties of Grassmannians
The Grassmannian G(1, 3)
An Analog of the Veronese Map
Incidence Correspondences
Varieties of Incident Planes
The Join of Two Varieties
Fano Varieties
Rational Functions and Rational Maps / Lecture 7:
Rational Functions
Rational Maps
Graphs of Rational Maps
Birational Isomorphism
The Quadric Surface
Degree of a Rational Map
Blow-Ups
Blowing Up Points
Blowing Up Subvarieties
The Quadric Surface Again
The Cubic Scroll in P[superscript 4]
Unirationality
More Examples / Lecture 8:
The Secant Plane Map
Secant Varieties
Trisecant Lines, etc.
Joins of Corresponding Points
Rational Normal Scrolls
Higher-Dimensional Scrolls
More Incidence Correspondences
Flag Manifolds
More Joins and Intersections
Quadrics of Rank 4
Rational Normal Scrolls II
Determinantal Varieties / Lecture 9:
Generic Determinantal Varieties
Segre Varieties
Secant Varieties of Segre Varieties
Linear Determinantal Varieties in General
Secant Varieties to Rational Normal Curves
Rational Normal Scrolls III
Rational Normal Scrolls IV
More General Determinantal Varieties
Symmetric and Skew-Symmetric Determinantal Varieties
Fano Varieties of Determinantal Varieties
Algebraic Groups / Lecture 10:
The General Linear Group GL[subscript n]K
The Orthogonal Group SO[subscript n]K
The Symplectic Group Sp[subscript 2n]K
Group Actions
PGL[subscript n+1]K acts on P[superscript n]
PGL[subscript 2]K Acts on P[superscript 2]
PGL[subscript 2]K Acts on P[superscript 3]
PGL[subscript 2]K Acts on P[superscript n]
PGL[subscript 3]K Acts on P[superscript 5]
PGL[subscript 3]K Acts on P[superscript 9]
PO[subscript n]K Acts on P[superscript n-1] (automorphisms of the Grassmannian)
PGL[subscript n]K Acts on P([logical and superscript k]K[superscript n])
Quotients
Quotients of Affine Varieties by Finite Groups
Quotients of Affine Space
Symmetric Products
Quotients of Projective Varieties by Finite Groups
Weighted Projective Spaces
Attributes of Varieties / Part II:
Definitions of Dimension and Elementary Examples / Lecture 11:
Complete Intersections
Immediate Examples
The Universal k-Plane
Secant Varieties in General
Joins of Varieties
(Some) Schubert Varieties
More Dimension Computations / Lecture 12:
Parameter Spaces of Twisted Cubics
Twisted Cubics
Twisted Cubics on a General Surface
Curves of Type (a, b) on a Quadric
GL (V) Acts on Sym[superscript d]V and [logical and superscript k]V
PGL[subscript n+1]K Acts on (P[superscript n])[superscript l] and G(k, n)[superscript l]
Hilbert Polynomials / Lecture 13:
Hilbert Functions and Polynomials
Hilbert Function of the Rational Normal Curve
Hilbert Function of the Veronese Variety
Hilbert Polynomials of Curves
Syzygies
Three Points in P[superscript 2]
Four Points in P[superscript 2]
Complete Intersections: Koszul Complexes
Smoothness and Tangent Spaces / Lecture 14:
The Zariski Tangent Space to a Variety
A Local Criterion for Isomorphism
Projective Tangent Spaces
Gauss Maps, Tangential and Dual Varieties / Lecture 15:
A Note About Characteristic
Gauss Maps
Tangential Varieties
The Variety of Tangent Lines
Joins of Intersecting Varieties
The Locus of Bitangent Lines
Dual Varieties
Tangent Spaces to Grassmannians / Lecture 16:
Tangent Spaces to Incidence Correspondences
The Variety of Secant Lines
Varieties Swept out by Linear Spaces
The Resolution of the Generic Determinantal Variety
Tangent Spaces to Dual Varieties
Tangent Spaces to Fano Varieties
Further Topics Involving Smoothness and Tangent Spaces / Lecture 17:
Gauss Maps on Curves
Osculating Planes and Associated Maps
The Second Fundamental Form
The Locus of Tangent Lines to a Variety
Bertini's Theorem
Blow-ups, Nash Blow-ups, and the Resolution of Singularities
Subadditivity of Codimensions of Intersections
Degree / Lecture 18:
Bezout's Theorem
The Rational Normal Curves
More Examples of Degrees
Veronese Varieties
Degrees of Cones and Projections
Unirationality of Cubic Hypersurfaces
Further Examples and Applications of Degree / Lecture 19:
Multidegree of a Subvariety of a Product
Projective Degree of a Map
Varieties of Minimal Degree
Degrees of Determinantal Varieties
Degrees of Varieties Swept out by Linear Spaces
Degrees of Some Grassmannians
Harnack's Theorem
Singular Points and Tangent Cones / Lecture 20:
Tangent Cones
Tangent Cones to Determinantal Varieties
Multiplicity
Examples of Singularities
Resolution of Singularities for Curves
Parameter Spaces and Moduli Spaces / Lecture 21:
Parameter Spaces
Chow Varieties
Hilbert Varieties
Curves of Degree 2
Moduli Spaces
Plane Cubics
Generalities about Quadrics / Lecture 22:
Tangent Spaces to Quadrics
Plane Conics
Quadric Surfaces
Quadrics in P[superscript n]
Linear Spaces on Quadrics
Lines on Quadrics
Planes on Four-Dimensional Quadrics
Fano Varieties of Quadrics in General
Families of Quadrics
The Variety of Quadrics in P[superscript 1]
The Variety of Quadrics in P[superscript 2]
Complete Conics
Pencils of Quadrics
Hints for Selected Exercises
References
Index
Preface
Acknowledgments
Using This Book
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