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Parshin A.N., Shafarevich I.R. — Algebraic Geometry III : Complex Algebraic Varieties. Algebraic Curves and Their Jacobians
Parshin A.N., Shafarevich I.R. — Algebraic Geometry III : Complex Algebraic Varieties. Algebraic Curves and Their Jacobians

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Название: Algebraic Geometry III : Complex Algebraic Varieties. Algebraic Curves and Their Jacobians

Авторы: Parshin A.N., Shafarevich I.R.

Аннотация:

The first contribution of this EMS volume on complex algebraic geometry touches upon many of the central problems in this vast and very active area of current research. While it is much too short to provide complete coverage of this subject, it provides a succinct summary of the areas it covers, while providing in-depth coverage of certain very important fields.The second part provides a brief and lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties, and partial differential equations of mathematical physics. The paper discusses the work of Mumford, Novikov, Krichever, and Shiota, and would be an excellent companion to the older classics on the subject.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 270

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, Niels Henrik      3 104
Action, monodromy,      129
Action, monodromy, semi-simplicity of      167
Airault, H.      226
Altaian, A.      110
Andreotti, Aldo      105 211 241 254
Arbarello, Enrico      233 239 241 259
Arnold, Vladimir      63
Artin, Michael      114
Axiom, covering homotopy      61
Beauville pair      246
Beauville, Armand      246 247 251 257
Bernoulli, Johann      3
Betti number      41 44
Betti number, even      41
Borel, Armand      210
Bott, Raoul      170
Brill — Noether number p      234
Bundle of conies      247
Bundle, antitautological      110 112
Bundle, canonical      54 99 117
Bundle, complexification of      25
Bundle, cotangent      24
Bundle, Hermitian, unitary basis of      30
Bundle, line      29
Bundle, line, associated to a divisor      50
Bundle, line, Chern class of      52
Bundle, line, negative      54
Bundle, line, positive      54
Bundle, normal      89 109
Bundle, tangent      14 24
Bundle, vector, $C^{\infty}$      29
Bundle, vector, Hermitian      30
Bundle, vector, holomorphic      28
Bundle, vector, orientable      25
Carlson, James A.      97 135 136
Cartan's Theorem B      157
Cartan, Henri      10 148
Catanese, Fabrizio      141
Cattani, Eduardo      97
Chakiris, Ken      115 126 127 129 141 142 212
Chart      19
Chern class      162
Chern class of a positive line bundle      68
Chern, S.S.      37
Chow's Lemma      21 143
Chow, C.K.H.C      20
Class, canonical      100
Class, canonical, of a K3 surface      115
Clemens — Schmid exact sequence      190 193 196 199 200
Clemens, Herbert      83 108 114 185 194 247 248
Co cycle, Cech      29
Cohomology with compact supports      63
Cohomology, primitive      43 60 68 130
Compactification, Baily — Borel      210
Compactification, proper      156 164
Compactification, semistable      129
Compactification, smooth      165
Complete linear system      50
Complex, simplicial      61
Conjecture, Donagi's      253
Conjecture, trisecant      257
Connection on a holomorphic vector bundle      30
Connection, affine      28
Connection, Gauss — Manin      89 176
Connection, locally integrable      89
Connection, matrix      31 34
Connection, metric      32 52
Coordinates, homogeneous      15
Cornalba, Maurizio      233 239 241
Covering, double      243
Covering, normal      244
Curvature matrix      31
Curve, algebraic      7
Curve, algebraic, Jacobian of      103
Curve, bi-elliptic      236 242 250
Curve, canonical      99 101
Curve, discriminant      113
Curve, elliptic      3 6 71 72 81 101
Curve, elliptic, j invariant of      72 101
Curve, elliptic, modular invariant of      102
Curve, hyperelliptic      94 101 105 141 226 231 246
Curve, hyperelliptic, Torelli theorem for      107
Curve, plane quintic      242
Curve, singular      7
Curve, special      235
Curve, symmetric power of      103
Curve, tetragonal      251
Curve, trigonal      237 242 250
Curve, unicursal      226
Cycle, finite      43
Cycle, invariant      9 195
Cycle, vanishing      62 63 66 167
Cycle, vanishing, space of      66
Dalalian, C.G.      246
de Concini, C.      259
de Rham, Georges      4 37
Debarre, Olivier      252 257
Decomposition, Lefschetz, of cohomology      43
Deformation      89
Deformation, analytic      84
Deformation, complete      91
Deformation, effective      91
Deformation, infinitesimal      91
Deformation, Kuranishi, versal      92
Deformation, locally trivial      90
Deformation, trivial      90
Degenerate fiber      183
Degeneration      183
Degeneration of curves      186
Degeneration of elliptic pencils      129
Degeneration of K3 surfaces      208
Degeneration of surfaces      199
Degeneration, semistable      129 183 184 190
Degeneration, semistable, of K3 surfaces      206
Deligne, Pierre      7 64 66 101 147 148 165 166 180 182 194 212
Differentiation, exterior      26
Divisor      49
Divisor of a meromorphic function      49
Divisor with normal crossings      156 178 183
Divisor with normal crossings, triple points of      156
Divisor, Chern class of      167
Divisor, effective      49
Divisor, linear equivalence of      50
Divisor, polarization      108 224 246
Divisor, principal      49
Divisor, regular      104
Divisor, theta      103 104
Donagi, Ron      97 129 134 136 179 247 252 253
Duality, Kodaira — Serre      38 44 57
Duality, projective      106
Duality, Serre      80
Dubrovin, B.A.      226
Eilenberg, Samuel      10 148
Embedding, Pluecker      110
Embedding, Veronese      137
Equation, algebraic, solution of      230
Equation, Cartan's structure      32
Equation, Korteweg — de Vries      225
Equation, local      49
Equation, local, of a sheaf      50
Equation, of Lax type      224
Equation, Toda lattice      229
Euler characteristic      142
Euler characteristic, algebraic      203
Euler characteristic, topological      205
Euler, Leonhard      3
Exact sequence, Clemens — Schmid      10
Exact sequence, long      8
Family of marked K3 surfaces      119
Family of polarized K3 surfaces      117
Family, algebraic, flat      101
Family, effective      96
Family, Kuranishi      91 96 128 142 178
Family, Kuranishi, universal      94 105 141
Family, Kuranishi, unpolarized      94
Family, smooth projective      85
Family, smooth, of a pair      178
Family, smooth, of complex analytic manifolds      61
Family, universal      91
Family, universal, of a polarized algebraic variety      95
Family, versal      91
Family, Weierstrass      129
Fano, G.      110
Fiber, degenerate      9
Fibration, locally trivial      60—62
Field of meromorphic functions      20
Filtration, Hodge      87
Filtration, stupid      164 169
Flow, Jacobian      224
Form, differential, positive      34
Form, harmonic      36
Form, holomorphic      4
Form, intersection      71
Form, Killing      77
Formula, adjunction      53 54 204
Formula, Hirzebruch's signature      175
Formula, Hurwitz      244
Formula, Kuenneth      148
Formula, Noether's      115 141 205
Formula, Picard — Lefschetz      63 66
Formula, Riemann — Roch      116 233 236
Formula, Umemura's      230
Fourfold, cubic,      108 139
Fourfold, cubic, rationality of      140
Fraction, meromorphic      18
Friedman, Bob      252
Froelicher, A.      91
Fulton, William      235
Function, analytic      17
Function, analytic, germ of      17
Function, holomorphic      17
Function, holomorphic, power series development of      17
Function, meromorphic      18
Function, rational      15
Function, rational, field of      12
Function, transition      28
Function, Weierstrass $\wp$      3
Functions, abelian      4
GAGA (Geometrie algebrique et Geometrie analytique)      9 19
Genus, arithmetic      186 211
Genus, geometric      46 141 173
Gieseker, David      237
Godement, Roger      10 148
Graded differential algebra      180
Graded differential algebra, augmentation ideal of      180
Graded differential algebra, connected      180
Graded differential algebra, elementary extension of      181
Graded differential algebra, minimal      181
Graded differential algebra, minimal model of      181
Graded differential algebra, simply connected      180
Grassmanian      5 69 76 87 110
Grassmanian, tangent bundle of      76
Green, Mark Lee      97 179 242
Griffiths, Phillip      10 66 70 77 78 83 86 88 95 97 108 114 129 133 135 136 147 179 180 182 185 212 233 236 239 241 248
Grothendieck, Alexandre      10 14 20 21 86 148 156 237
Group, fundamental      62
Group, monodromy      62 66 85 86
Group, monodromy , of an extended variation of Hodge structures      89
Group, Picard      51
Group, Picard (PicX)      30
Gunning, Robert      19 257 258
Gusein-Zade, Sabir      63
Hain, Richard M.      183
Halfplane, upper      71 102
Halfplane, upper, Siegel      71 74 102 254
Harris, Joe      10 233 236 239 241
Hartshorne, Robin      14
Hilbert, David      11 13
Hironaka, Heisuke      16 22 156
Hirzebruch, Fritz      175
Hodge      5
Hodge structure      5 66 67 75
Hodge structure of odd weight      77
Hodge structure on an elliptic pencil      128
Hodge structure on the cohomology of smooth hypersurfaces      168
Hodge structure, extended variation of      89 96 102 126
Hodge structure, infinitesimal variation of      97 135
Hodge structure, limit      188
Hodge structure, mixed      7 8 143 145—147 154 176
Hodge structure, mixed, on homotopy groups      180
Hodge structure, mixed, on the cohomology of smooth varieties      156
Hodge structure, mixed, with graded polarization      177
Hodge structure, polarized      9 67 74 75 78 79 84 86
Hodge structure, pure      144
Hodge structure, variation of      88
Hodge structure, variation of mixed      176
Hodge structure, weighted      67
Hodge — Riemann bilinear relations      44 67 68 70 116 142 143
Hodge, *operator      35
Hodge, canonical bundle      77
Hodge, decomposition      5 6 41 68 84
Hodge, filtration      5 8 145 160
Hodge, filtration, decreasing      67
Hodge, filtration, limit      189
Hodge, number      68
Hodge, numbers      5 41 85 168 173
Hodge, numbers, of complete intersections      175
Hodge, numbers, of smooth hypersurfaces      174
Homotopy      61
Homotopy groups, mixed Hodge structures on      180
Homotopy groups, Whitehead product on      182
Hopf, Heinz      42 194
Hoyt, William L.      254
Hypercohomology      156 168
Hypersurface      49 129
Hypersurface, algebraic      11
Hypersurface, cubic      82 139
Hypersurface, fundamental class of      53
Hypersurface, smooth      173
Ideal, associated to an algebraic set      11
Igusa, Jun-ichi      259
Integral, abelian      3
Integral, elliptic      3
Invariant, modular      102
Iskovskikh, V.A.      252
Isomorphism, bi-rational      16
Isomorphism, holomorphic      17
Jacobi, Carl      3
Jacobian      80
Jacobian ideal      130
Jacobian, intermediate      79 247
Jacobian, intermediate, Weil      82
Jacobian, middle      79 83
Jacobian, middle, polarized      108
Jacobian, polarized      103
Jung, H.      259
Kadomtsev — Petviashvili (KP) hierarchy      227 258
Kahler, Erich      5
Kanev, V.I.      252
Kaplan, Aroldo      97
Kashiwara      178
Kay, I.      226
Kempf, George      184 234 243
Kii, K.I.      127 128
Kleiman, Steven      110 234
Kodaira dimension      126
Kodaira, Kunihiko      21 46 55 91 123 187
Koszul complex      131
Krichever, Igor      224 258 259
1 2 3
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