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Clemens C.H. — Scrapbook of Complex Curve Theory

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Название: Scrapbook of Complex Curve Theory

Автор: Clemens C.H.

Аннотация:

First published in 1980, this monograph covers a range of basic issues in the classical subject of compact Riemann surfaces. The material was selected according to the author's fancy, but he identifies the theory of theta functions as a primary theme. Topics include conics, cubics, theta functions, the Jacobian variety, quartics and quintics, and the Schottky Relation. Although the work has not been revised, an addendum listing references to the subsequent literature has been provided.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1980

Количество страниц: 196

Добавлена в каталог: 01.06.2008

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Предметный указатель

— Invariant      102 105
— Geometry      30
$\breve{C}$ ech cochain      70
$\breve{C}$ ech one-cochain      119
Abelian varieties      134 175
Abel’s theorem      82 122 127
Absolute, the      17 28
Accola      vi 175
Affine set      8
Affme-coordinates      40
Albanese variety      122
Analytic continuation      53
Analytic manifold      53
Andreotti      145 159
Anharmonic lines      30
Associativity of cubic group law      44
Automorphic form      104 (see also Modular forms)
Automorphism      100
Automorphism of elliptic curve      94 95
Base locus      176
Basepoint      55
Beauville      vi
Bezout’s Theorem      12
Bitangents      150
Blowing up a point      47
Branch point      52 145
Canonical bundle      140 158
Canonical divisor      140 152 175
Canonical mapping      151 175
Cap product      124
Cardinality      63 67
Cartan      vi
Cauchy integral formula      55
Cayley      17
Cell complex      113
Character formula      63
Characters      167
Chern class      118 139
Chinese remainder theorem      35
circle      30
Cohomology groups      134
Complex conjugation      50
Complex manifold      66 69 70 105
Component      12
Cone      6 18 176
Congruence      64
conic      8 9 17
Conic, through five given points      11
Contact      39 77
Coordinates, affine      8
Coordinates, homogeneous      8
Cotangent bundle      55 140
Cotangent space      66
Covering group      134
Covering space      58 89
Cremona transformation      48
Cross ratio      13 18 28 52 91 93
Cubic      12 37 73 82 89
Cup-product pairing      116
Curvature      20
Curvature, Euclidean      31
Curvature, geodesic      31
Curve, cubic      95
Curve, elliptic      75 91 94 95 96
Cusp      154
Cusp form      112
Deformation      172
deRham cohomology      59 66
deRham complex      66
Desingularization      78
Differential      54 89
Differential equation      59
Differential forms      115 125
Differential, abelian      53
Differential, exact      60
Differential, holomorphic      152
Differential, meromorphic      137
Differential, Prym      163
Divisor      84
Dolbeauit complex      66
Double complex      70 115 120
Double points      154
Dual curve      24
Dual mapping      152
Eisenstein series      87
ellipse      1
Elliptic integral      55
Euclid’s fifth postulate      17
Euler characteristic      55 101 145 154
Euler’s formula      23 38
Family of curves      147
Farkas      vi 161
Fibered product      52
Finitely generated abelian group      50
Fourier coefficients      136
Fourier expansion      78
Fourier series      89 136 166
Fourier transform      107
Framing      94 95
Frobenius mapping      67
Function, meromorphic      51 78 80 82 137
Function, rational      75
Function, theta      73 106 132 159 164
Function, trigonometric      85
Fundamental domain      80 96 109 110 134
Fundamental group      161
Gauss map      151 155
Genus      114 149
Geodesic      20 27
Geometry, differential      54
Geometry, of constant curvature      17
Geometry, plant      15
Geometry, Riemannian      17 33
Grassmann variety      153
Green’s Theorem      56
group of      21
Group of rational points      45
Gunning      115 118 132
Hessian curve      39 152
Hirzebruch      125
Hodge theory      115
Homogeneous equation      5
Hyperbola      1
Hyperbolic geometry      21 26 32
Hyperelliptic curve      151 155
Igusa      vi
Implicit function theorem      54
infinity      40 50

Inflection points      37
Intersection pairing      102 162
Invariant      14
Invariant, global      66
Invariant, local      66
Involution      162 175
Isometries      167
Isomorphism class      93 95 97
Jacobi inversion theorem      131 136
Jacobian matrix      65 153
Jacobian variety      113 123 127
Jacobi’s identity      111
K $\breve{a}$ hler manifold      66 115 125
Kodaira      145 158
Lattices      165 170
Laurent series      86 88
Law of the sine      13
Lefschetz duality      122
Lefschetz flxed-point theorem      65
Lefschetz number      65
Lewittes      144
Lie group      131
Line bundles      113 142
Line integral      56
Linear fractional transformation      95
Linear systems      138 176
Lorentz transformations      22
Manin      vi 65
Mayer      145 159
Metric      120
Metric, Euclidean      32
Metric, induced      19
Modular forms      73 87 105 106 109 112
Moduli space      53 91 96 101 145
Monodromy group      92
Mordell's Theorem      50
Multiplicity of a point      142
Mumford      vi 134
Mystic hexagon      11 26
Nondegenerate plane curve      24
Nonsingularity      147
Normalization      156
Orthonormal basis      165
parabola      1
Parametrization      75
Parametrization, rational      76
Pencil      176
Period      59
Period matrix      164 168 174
Perpendicularity      6 27
Picard variety      115 122
Picard — Fuchs equation      58 64 68
Picard’s Theorem      98
Poincar $\acute{e}$ mapping      123 129 142
Poincare dual      116
Point, infinitely near      78
Point, singular      76 77
Poisson summation formula      89 108
Polar coordinates      56
Polar curves      22
Polar mapping      24 29 37
Polar of a point      25
Pontryagin product      124 131
Power-series expansion      62
Projection      176
Projective line      18
Projective plane, complex      8
Projective plane, real      148
Projective set      8
Projective space      103 132 151
Projective space, complex      7
Projective space, real      5
Projectivization      8
Prym varieties      161 171 178
Quadratic form      133
Quadrics      176
Quarries      147
Quintics      158
Ramification      89
Ramification point      43
Rational points      33 62
Rauch      vi
Regular singular points      61
Residue      59
Resultant      9
Riemann      133
Riemann relation      58 78 117 163
Riemann sphere      80
Riemann surface      147 175
Riemann — Roch theorem      68 85 87 95 128 136 151
Riemann’s constant      137 139
Riemann’s singularities theorem      142 159 178
Riemann’s theorem      136
Riemann’s theta relation      111 165 167
Scalar product      165
Schottky      163
Schottky relation      164 174 178
Schottky — Jung      173 178
Serre      vi 87 105 132 145
Serre duality      68 69
Sheaf      67
Sheaf cohomology      66 113
Sheaf of holomorphic tunctions      114
Skew — Hermrtian matrix      126
Spectral sequence      115
Spencer      145
Spherical distance      19
Spherical geometry      26
Steieogiaphic projection      26 33 42 51 76
Surface integral      56
Symmetric product      25 52 131
Symplectic basis      102 114 133
Tangent cone      77 160
Tangent line      154
Tangent spaces      150
Tate      44 46 73
Theta Characteristics      140 143 155 157 158 171 177
Theta functions      132
Theta-null      89 106 109
Tjurin      158
Topological group      43
Torus      43
Transversality      65
Unbranched double covering      160 161
Universal covering spaces      133
Upper half-plane      97 103
Van Der Monde determinant      10
Wedge algebra      124
Weierstrass -function      58 85 87

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