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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
Kulikov, N.S.      199
Kulikov, Vik, S.      199
Kulikov, Viktor      96 115 205
Kuranishi, M.      86 91 92
Kynev, V.I.      141
Laksov, Dan      234
Landman, Alan      168 185 189
Laplacian      36
Laplacian, $\bar{\partial}$      57
Lattice      72
Lattice, Euclidean      118 127
Lattice, Euclidean, even      118
Lattice, Euclidean, unimodular      118 139
Lazarsfeld, Rob      235
Lefschetz decomposition      42 60
Lefschetz duality      192
Lefschetz, Solomon      43
Legendre, Adrien Marie      3
Lemma, $\partial \bar{\partial}$      55
Lemma, Poincare      26 159
Lieberman, David I.      82
Linear system, complete      101
Macaulay, F.S.      131
Manifold, complex      5 19
Manifold, complex deformation of      89
Manifold, complex degenerations of      183
Manifold, complex orientability of      25
Manifold, complex rigid      91
Manifold, complex with normal crossings      149
Manifold, flag      5 70
Manifold, Hermitian      33
Manifold, Hodge      46
Manifold, Hopf      42
Manifold, Kaehler      5 38
Manifold, non-algebraic, with a maximal number of Meromorphic functions      23
Manifold, smooth      24
Map, Gysin      163 169
Mapping, Abel — Jacobi      81 111
Mapping, Abel — Jacobi, regularity of      82
Mapping, Albanese      80 81 112
Mapping, Albanese, holomorphic      103
Mapping, canonical      100 101 104 107
Mapping, Clemens      185 192
Mapping, cylindrical      112
Mapping, Gauss      105 108 239
Mapping, Gysin      161
Mapping, holomorphic      17
Mapping, Kodaira — Spencer      89—91 96 98 117 120 178
Mapping, period      6 7 66 84 86 95 134 167
Mapping, period, closed points of      105
Mapping, period, for algebraic curves      100
Mapping, period, for K3 surfaces      205 209
Mapping, period, for the smooth family of a pair      178
Mapping, period, holomorphic      120
Mapping, period, surjectivity of      96
Mapping, Poincare residue      168
Mapping, Prym      252
Mapping, rationa      15
Mapping, regular      11
Mapping, Veronese      138
Mapping, Veronese, canonical      104
Martens, Henrik      241
Masiewicky, L.      247
Matrix, Brill — Noether      233
Matrix, Siegel      258
Matve'ev, V.B      226
McKean, Henry      226
Metric, Fubini — Study      39 53 55
Metric, Hermitian, associated form of      33
Metric, Kaehler      24 38
Metric, Riemannian, on a Hermitian manifold      33
Meyer, A.      254
Milnor, John      63
Module, irreducible      42
Module, totally reducible      42
Moduli      4 93
Moduli space      92 93
Moduli space of a quartic hypersurface      116
Moduli space of hyperelliptic curves      94
Moduli space of K3 surfaces      94
Moduli space of marked K3 surface      120
Moduli space of nonsingular hypersurfaces      132
Moduli space of nonsingular hypersurfaces, closed points of      132
Moduli space of polarized abelian varieties      75 94
Moduli space, closed points of      103
Moduli space, coarse      93 101
Moduli space, coarse, closed point of      101
Moduli space, fine      93
Moishezon, Boris      21 24 186
monodromy      60
Morgan, John      180 182 183 212
Morphism      11
Morphism of mixed Hodge structures      145
Morphism of pure Hodge structures      144
Morphism of weighted Hodge structures      144
Morphism, smooth, proper      61
Morphism, strict      144
Moser, Juergen      226
Moses, H.      226
Mumford, David      75 80 93 101 103 114 132 184 189 203 224 246 250
Namikawa      187
Neighborhood, coordinate      19
Nickerson, Helen      159 162
Nijenhuis, A.      91
Nirenberg, Leon      91
Novikov, Sergei      226 259
Nullstellensatz      11 13
Ogg, Andrew P.      187
Operator, compact      228
Operator, compact self-adjoint      37
Operator, elliptic      36
Operator, finite difference      228
Operator, finite-dimensional      227
Operator, Green — de Rham      37
Operator, Griffiths      79
Operator, harmonic projection      36
Operator, Laplace      36
Operator, linear differential      222
Operator, Poincare residue      130 158
Operator, pseudo-differential      225
Operator, Weyl      68
Operators, commuting      221
Orientation of a differentiable manifold      26
Oriented vector space      25
Pencil, elliptic      115 126
Pencil, elliptic, special      127 128
Pencil, Lefschetz      64 65
Period      4 5
Period, lattice      4
Period, matrix      4
Persson, Ulf      199 204
Petri, Alberto      239
Piatetsky-Shapiro, Ilya      115 119 121
Plane, affine      3
Plane, projective      3
Poincare duality      43
Point, closed      96
Point, non-singular      13
Point, regular      18
Point, smooth      13
Polarization      68
Polarization, principal      75
Polyhedron of a variety with normal crossings      154
Problem, Luroth      83 108 251
Problem, Schottky      259
Problem, Torelli      89
Problem, Torelli, generic      89
Problem, Torelli, global      89
Problem, Torelli, infinitesimal      89
Problem, Torelli, local      89
Problem, Torelli, weak      89
Property, local lifting      86
Prymian      243 244
Radical      11
Recillas, S.      251
Relation, Schottky's      259
Representation, monodromy      62
Resolution, fine      56
Riemann surface, compact      21
Riemann — Frobenius conditions      47 72
Riemann, Bernhard      21 93 104
Ring of regular functions      11
Ring, local      12
Rossi, Hugo      19
Saito, Masa-Hiko      177—179
Scheme      14
Schmid, Wilfried      147 188—190
Schottky, F.      259
Section, holomorphic      28
Sequence, Mayer — Vietoris      149
Sequence, spectral      27 148 152
Sequence, spectral, hypercohomology      27
Sequence, spectral, Leray      166
Serre, Jean-Pierre      10 20 21 118 127
Set, algebraic      11
Set, algebraic, category of      12
Set, algebraic, irreducible      12
Set, analytic      17
Set, analytic, irreducible      18
Set, analytic, irreducible at a point      18
Set, Zariski open      12
Shafarevich, Igor      12 14 115 119 121 205
Sheaf of complex differential forms      26
Sheaf of differential forms      29
Sheaf of holomorphic differential forms      27
Sheaf of holomorphic n-forms with logarithmic poles      157
Sheaf of meromorphic functions      50
Sheaf of rings      13
Sheaf of sections of a holomorphic vector bundle      29
Sheaf, canonical      85
Sheaf, coherent      20
Sheaf, coherent, flat      203
Sheaf, fine      26
Sheaf, grassmanization of      98
Sheaf, Hodge      77
Sheaf, horizontal      99
Sheaf, locally constant      8
Sheaf, normal      109
Sheaf, structure      13
Sheaf, tautological      76
Shimizu, Yuji      177—179
Shiota, Tak      223 224 226 259
Shokurov, V.V.      242 252
Siegel modular forms      231
Siegel, Carl-Ludwig      20 177 178
Singularity, non-degenerate quadratic      62 64
Singularity, resolution of      7
Singularity, simple      62
Smith normal form      72
Smith, R.      247 252
Soliton, Airault — McKean — Moser rational      226
Soliton, Kay — Moses      226
Space of period matrices      6
Space, analytic      92
Space, classifying      6 67 76
Space, classifying, of a non-singular projective curve      70
Space, classifying, of period matrices      84
Space, classifying, of polarized Hodge structures      69 71 120
Space, classifying, of weighted Hodge structures      142
Space, classifying, structure of flag manifold on      70
Space, complex      18 21
Space, complex projective      19 39
Space, holomorphic      25
Space, moduli, of polarized algebraic varieties      94
Space, moduli, of principally polarized abelian varieties      75
Space, projective $(P^n)      $14
Space, ringed      14
Space, tangent      13
Spencer, D.C.      91
Steenbrink, J.      85 188 194 195
Subbundle, horizontal      177
Subbundle, tautological      110
Subspace, horizontal      76
Sullivan, Dennis      180 182 212
surface      141
Surface, algebraic, polarized      75
Surface, cubic      108 109
Surface, cubic, rationality of      109
Surface, cubic, twenty seven lines on      109
Surface, elliptic, Euler characteristic of      123
Surface, elliptic, special      127
Surface, Enriques      115
Surface, Fano      82 110
Surface, K3      94 115
Surface, K3, marked      119 121
Surface, Kummer      116
Surface, Kummer, special      116 121 122 125 127
Surface, modular      72
Surface, quartic      116
System, local      176
Theorem, Abel's      104
Theorem, Andreotti — Meyer      254
Theorem, Bertini's      64 123 235
Theorem, Bott's      170
Theorem, Chow's      20
Theorem, Clifford's      242
Theorem, de Rham for varieties with normal crossings      151
Theorem, de Rham's      26
Theorem, Dolbeault's      27 157
Theorem, hard Lefschetz      43 60 154 166
Theorem, Hironaka's      156 164 183 210
Theorem, Hodge index      69
Theorem, implicit function      19
Theorem, index      46
Theorem, invariant subspace      165
Theorem, Kempf's      243
Theorem, Kodaira embedding      46
Theorem, Kodaira embedding for surfaces      21
Theorem, Kodaira vanishing      54 58
Theorem, Landman's      168
Theorem, Lefschetz      113 176 235
Theorem, Lefschetz on hyperplane sections      54 59
Theorem, Lefschetz' on hyperplane sections      59
Theorem, M.Green's      242
Theorem, Macaulay's      131
Theorem, Martens      241 250
Theorem, Mumford's      242
Theorem, Noether — Castelnuovo      141
Theorem, Petri — Gieseker      239
Theorem, Riemann — Roch      100 104 122 123
Theorem, Riemann's      104
Theorem, Riemann's on singularities      242
Theorem, semistable reduction      184
Theorem, Shiota's      259
Theorem, Siegel's      21
Theorem, Stokes'      53
Theorem, Sturm's      231
Theorem, Torelli      240 257
Theta divisor      103
Theta function, Riemann's      227
Threefold, cubic      83 84 108 248
Todorov, Andrei      141 142 212
Topology, complex      16
Topology, Zariski      11
Torelli theorem      5 6 100 106 140
Torelli theorem for cubic threefolds      108
Torelli theorem for curves      104
Torelli theorem for hyperelliptic curves      107
Torelli theorem for the cubic threefold      114
Torelli theorem, generalized      96
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