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Eisenbud D., Harris J. — The geometry of schemes (textbook draft)
Eisenbud D., Harris J. — The geometry of schemes (textbook draft)

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Название: The geometry of schemes (textbook draft)

Авторы: Eisenbud D., Harris J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Количество страниц: 299

Добавлена в каталог: 06.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_2$ singularity      204
Absolutely irreducible      56
Acnode      57
Affine, line      48
Affine, locally      21
Affine, pair      22
Affine, plane      48
Affine, scheme      7 8 21 30
Affine, scheme primary      68
Affine, schemes and commutative rings      36
Affine, space      33 34 47 84
Affine, tangent space      104 105
Affine, variety      47
Algebra coordinate      28 47
Algebra dimension of      32 60
Algebra division      207
Algebra graded      91 95 100 101 170
Algebra Noetherian      81
Algebra quasicoherent sheaf of-s      40 101
Algebra reduced      47 53
Algebra Rees      172 173
Algebra spectrum of      40 111
Algebra symmetric      102 105 122 173
Algebra, Azumaya      206
Algebraic geometry      (see Classical)
Algebraic geometry spaces      262
Algebraic geometry stack      276
Algebraically closed      8—11 47 48 50 58 62 65 83 104 119 123 140 141 151 153—156 160 163 178 191—193 195 203 207 213 228 231 239 243 245 248 272 276
Alonso, Leo      5
Altman, Allen      230
Analytic, branch      52
Analytic, functions      27
Analytic, functions, sheaf of      14
Analytic, manifold      8 51
Analytic, spaces      116
Annihilator sheaf      220
Arithmetic, genus      129 138
Arithmetic, scheme      81 110 162 180 185 188 245 249
Artin, Michael      53 261
Artinian ring      65 78
Associated to a variety      47
Associated, closed ideal      100
Associated, prime      67
Associated, scheme      68
Axiom of Choice      12
Azumaya algebra      206
Base of open sets      16
Base, change      38 54 152 154 168 209 213 216 219 221 222 236 237 241
Base, Groebner      75
Base, scheme      45 95 122 193 222
Basic open set      10 14 16 30
Bayer, David      138
Behrend, Kai A.      277
Betti number      127 128 130
Bezout’s Theorem      141 146 148 154
Blow-up      103 162—192
Bombieri, Enrico      1
Bourbaki, Nicolas      76 112
Brauer group      206
Brieskorn, Egbert      52
Brill — Noether — Petri problems      1
Brown, Edgar H.      261
Buhler, Joe      5
Burch, Lindsay      133
Cartier, divisor      110 117 166 167 174
Cartier, subscheme      165 167 168 175 176 178 182
Cassels, J. W. S.      206
Castelnuovo regularity      264
Categorical, definition of morphism of sheaves      15
Categorical, definition of presheaf      12
Categorical, equivalence of affine schemes and rings      30
Category of algebras      253 258
Category of rings      30
Category, opposite      30
Center of blow-up      165
Chevalley, Claude      210
Chinese remainder theorem      60
Choice, axiom of      12
Classical, algebraic geometry      8 9 28 34 40 47 49 57 59 94 109 114 117 119 120 125 138 140 141 148 151—154 156 161—165 180 184 192 193 197 210 222—224 231—233 240 242 246—248
Clemens, Herbert      5 179
Closed, locally      26
Closed, point      11 22 26 31 42 48 50—52 54—56 60 63 70 71 75 76 82 83 85 88 93 105 111 132 160 191 216 239 247 255 256 274 275
Closed, subfunctor      255
Closed, subscheme      23 24 71 100 211
Closed, universally      95
Closure      26
Coarse moduli space      276
Cohen — Macaulay      32 146 151
Coherent sheaf      24 25 103
Cokernel      16
Collino, Alberto      265
Commutative ring      (see Ring)
Compactness      19 91 93—95 229
Compatibility condition      33
Complement of a subfunctor      255
Complex, manifold      8 20
Component, embedded      66 68
Component, isolated      67 68
Component, length of      68
Component, multiple      156
Component, primary      67 68
Cone, cubic      63
Cone, over a cubic      204
Cone, over a quartic      148
Cone, quadric      173 175 197—199
Cone, tangent      106—110 171 178 190 192 203 204
Cone, tangent projectivized      107
conic      63 86 141 142 160 179 185 186 190 196 198 202
Conic and quartic      160
Conic double      138 156 157
Conic, intersection with line      59
Conic, reducible and nonsingular      87
Conic, universal      207 208
Constructible, subset      209
Containment of schemes      23
Continuous, functions, sheaf of      13
Coolidge, Julian L.      152 242
Coordinate ring      47
Cotangent, sheaf relative      231
Cotangent, sheaf, relative      230
Cotangent, space, Zariski      27
Cox, David      229
Crunode      57
Cubic, lines on      202
Cubic, surface      191
Cubic, universal      203 204
Curvilinear, scheme      65
Cusp      156 239
Decomposition, primary      67 68
Dedekind domain      71 75
Deformation, first-order      267
Degree of affine scheme      62 65
Degree of scheme      129 141
Degree of subscheme      125
Dehomogenization      98 153
Deligne, Pierre      1
Demazure, Michel      261
Diagonal subscheme      93
Dieudonne, Jean      5
Different of a polynomial      234
Dimension of scheme      27
Dimension, Krull      27 65
Dimension, relative      231
Direct limit      14
Discriminant of a polynomial      233
Discriminant, scheme      231
Distinguished open set      10 23
Division algebra      207
Divisor, Cartier      117
Divisor, exceptional      164 165
Dominant morphism      211
Double, conic      138
Double, line      136
Double, point      58 62 88 178 180 246
Dual, curve      162 237 240
Dual, projective space      103
Effective Cartier divisor      117
Elemination theory      210
Eliot, Thomas Stearns      v
Elliptic curve      161
Embedded, component      66 68
Embedded, point      66
Equalizer      35
Equations with parameters      70
Etale, equivalence relations      262
Etale, Euler’s relation      153
Etale, topology      53
Exceptional divisor      164 165
Faithful functor      43
Faltings, Gerd      1
Family of closed subschemes      71
Family of curves      156
Family tangent space to      271
Family universal      203
Family variety, universal      204
Family, flat      75
Family, limit of      71
Family, universal      222
Fano, scheme      120 193—205 266 273
Fantechi, L.      277
Fiber      31 38 49 70
Fibered, coproduct      37
Fibered, product      35 36 254 260
Fibered, sum      37
Finite, morphism      92
Finite, scheme      62
Finite, type      76 210 231
Finite, type, morphism of      92
Finitely generated      8 47 50
First-order, deformation      267
First-order, neighborhood      58 67
Fitting’s Lemma      219
Fitting’s Lemma, ideal      220 221 225 231 232 236 238
Fitting’s Lemma, image      219 221—224
Fitting’s Lemma, scheme      220
Flat, family      75 125
Flat, limit      77
Flat, module      75
Flat, scheme      32
Flatness, geometric interpretation of      125
Flatness, theorem      79
Flex      151 152
FLOP      179
Fong, Lung — Ying      138
Form (type of scheme)      205
Forster, Otto      18
Four Quartets      v
Free resolution      127 128 133 134 144
Frobenius automorphism      56
Frohlich, Albrecht      206
Fulton, William      148 277
Functor of nonsingular curves      274
Functor of points      42 43 252
Functor, faithful      43
Functor, injective      254
Functor, representable      44
Functor, tangent space to      256
Gabriel, Pierre      261
Galois, cohomology      206
Galois, group      40 56 85 87
Gashorov, Vesselin      5
Gathmann, Andreas      5
Generic, flatness theorem      79
Generic, hypersurface      123
Generic, point      9 48
Genus, arithmetic      129 138
Geometrically irreducible      56
Germ of analytic function      14
Germ of variety      50
Global, Proj      102 170
Global, regular function      22
Global, section      12
Global, Spec      40 41
Gluing      33
Godement, Roger      18
Gottsche, Lothar      277
Graber, Tom      5
Graded ring, Proj of      95
Graded, algebra      91 95 100 101 170
Graded, Betti number      127
Graded, Betti numbers      128 130
Graded, module      118
Graded, sheaf      118
Grading      34 96
Grassmannian      63 119 193 195 201 206 207 261 263 264 272 273
Grassmannian, functor      261
Green, Mark L.      130
Griffiths, Phillip      1 155 192 203
Grobner bases      75 229
Gross, Benedict      5
Grothendieck, Alexandre      1 5 18 79 261
Group scheme      258
Gruson, Laurent      77
Gunning, Robert C.      18
Hartshorne, Robin      4 5 18 75 95 101 110 125 126 129 155 162 210 218
Hassett, Brendan      5
Hausdorff      11 19 91 93 95
Henselization      52
hessian      153—155 157
Hilbert, David      48 125 128
Hilbert, function      124—130
Hilbert, functor      262
Hilbert, polynomial      125 129 130 143 262—264
Hilbert, scheme      120 129 259 262 264 266
Hilbert, series      149 150
Hilbert, tangent space to      267
Hilbert, theorem      125
Hilbert, theorems      128
Hironaka, Heisuke      261
Homogeneous, coordinate ring      96
Homogeneous, element      96
Homogeneous, ideal      96
Homogenization      98
Hyperplane, universal      124
Hypersurface      122 141
Hypersurface, generic      123
Hypersurface, universal      123
Iarrobino, Anthony      64 265
Ideal      (see Prime maximal)
Ideal of minors      219
Ideal, Fitting      220 221 225 231 232 236 238
Ideal, sheaf      24
Image of morphism      209
Image, Fitting      219 221—224
Image, reduced      222
Image, scheme-theoretic      222 223
Image, set-theoretic      209 222
Infinitely near point      59
Injective functor      254
Intersection      151
Intersection of a flex      154
Intersection of associated scheme      68
Intersection of conics      143
Intersection of intersection      141
Intersection of point      60
Intersection of ring      66
Intersection of scheme      65 66
Intersection of schemes      24
Intersection, multiplicity      141 148 151
Invariance under base change      209
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