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| Eisenbud D., Harris J. — The geometry of schemes (textbook draft) |
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| Предметный указатель |
Invariants of projective scheme 124
Inverse of a sheaf 117
Inverse, image (see Preimage)
Inverse, limit 17 53
Invertible, module 113
Invertible, sheaf 112 116 117
Irreducible scheme 25
Irreducible scheme, absolutely 56
Irrelevant ideal 96
Isolated component 67 68
J-function 184
J-invariant 185 205 275 276
Jacobian 230 231
Jeremias, Ana 5
Join 147
Kahler differentials 230
Kempf, George R. 33
Kleiman, Steven 118 230
Knorrer, Horst 52
Knutson, Donald 262
Kollar, Janos 1 179 263
Koszul complex 143 144 173
Kresch, A. 277
Krull dimension 27 39 65
Krull, Wolfgang 28
Lang, Serge 234
Lazarsfeld, Robert 130
Leading term 107
Lee, Alex 5
Lefschetz hyperplane theorem 124
Length of component 68
Length of module 68
Length of ring 66
Length of scheme 66
Levy, Silvio 5
Lie group 161
Limit of one-parameter family of schemes 71
Limit, direct 14
Limit, flat 77
Limit, inverse 17 53
Little, John 229
Local of a scheme 22 27
Local, homomorphism 30
Local, ring 30 51 65
Local, ringed space 22
Local, scheme 50
Locally, affine 21
Locally, closed subscheme 26
Locally, complete intersection subschemes 146
Locally, free module 112
Locally, induced 16
Locally, Noetherian 253
Manifold 8
MAP (see Morphism)
Matsumura, Hideyuki 75—77 79 128
Maximal, ideal 9—11 27 30 31
Mederer, Kurt 5
Minimal prime 25 26
Minors, ideal of 219
Module, flat 75
Module, length of 68
Moduli space 274 276
Monodromy group 143
Mordell, conjecture 1
Mori, Shigefumi 1 179
Morphism 40
Morphism of schemes 28 29
Morphism of schemes over S 40
Morphism of sheaves 15
Morphism to projective space 110 5
Morphism, dominant 211
Morphism, image of 209
Morphism, projective 97 101
Morphism, proper 95
Morrison, David 1
Multiple, component 242
Multiple, components 156
Multiple, line 80
Multiple, point 62 182
Multiplicity 107
Mumford, David 1 5 78 192 263 270 277
Mustata, Mircea 5
Nagata, Masayoshi 56
Nakayama’s Lemma 62 126 128 166 171 217 218
Nash manifold 8
Nilpotent-free (see also Reduced)
Nilradical of a ring 25
Nilradical of a scheme 25
Node 57 156 239
Noetherian, algebra 81
Noetherian, ring 19 26 28 67 130 172 253
Noetherian, scheme 26—28 183 210 231
Nonaffine scheme 22 33
Nonalgebraically closed 53 57 65 84 142 152 191 193 195 201 241
Nonclosed point 42 48 51 56 85 87 114
Nonreduced scheme 57 180
Nonsingular, curves, functor of 274
Nonsingular, scheme 28
Normal sheaf 268
Northcott, D. G. 67
Nullstellensatz 48 54
Number field 82
Ogus, Arthur 5
Open, covering, of a functor 255
Open, subfunctor 254
Open, subscheme 23
Opposite category 30
Order (in a number field) 84 188
Ordinary, double point 178
Ordinary, node or tacnode 239
Over K, scheme 39
Over something, scheme 40
Parameter spaces 262
Parameters, equations with 70
Pardue, Keith 5
Partition of unity 20
Peeva, Irena 5
Pell’s equation 205
Pencil of cubics 184 204
Pencil of plane curves 185
Pencil of quadrics 201
Plane curve 123 152
Pliicker, coordinates 207
Pliicker, equations 120 121
Pliicker, formulas 156 242
Pliicker, ideal 122
Pliicker, relations 121
Power series 14 52 53 71
Preimage 38 49 52
Presheaf 11
Presheaf of modules 12
Primary, affine scheme 68
Primary, component 67 68
Primary, decomposition 67 68
Primary, ideal 67
Prime 9
Prime, associated 67
Prime, ideal sheaf 41
Prime, minimal 25
Product of graded ring 95
Product, fibered 35 254
Projective, bundle 103
Projective, dual 103
Projective, invariants of 124
Projective, module 113
Projective, morphism 97 101
Projective, scheme 91 95
Projective, space 34 35 96
Projective, space, morphisms to 110
Projective, tangent 152
| Projective, tangent space 104 105
Projectivization 103
Projectivization of coherent sheaf 103
Proper, map of Hausdorff spaces 95
Proper, morphism 95
Proper, transform 168
Properness 19
Pullback 35
Push-pull property 209 210
Pushforward 18
Quadratic form 53
Quadric, cone 197—199
Quadric, degeneration 199
Quadric, lines on 195
Quadric, surface 191
Quadric, universal 202
Quasicoherent sheaf 24 25
Quasicoherent sheaf of graded algebras 101
Quasicompactness 19 93
Quaternions 206
Radical 67
Ramification 83
Rational, function 20 52
Rational, over K 45 256
Raynaud, Michel 77
Reduced, algebra 47 50 53
Reduced, image 222
Reduced, ring 26
Reduced, scheme 25 47 53 68
Rees algebra 172 173
Regular, function 10 22
Regular, global 22
Regularity 251
Reid, Miles 5
Relative, cotangent sheaf 230 231
Relative, dimension 231
Relative, Hilbert scheme 266
Relative, scheme 35
Relevant ideal 96
Representable, functor 44
Representable, scheme 252
Residue field 9
Resolution, free 127 128 133 134
Resolution, small 179
Restriction 11 13
Resultant 213 219 222—224
Riemann, sphere 15
Riemann, surface 83 129
Ring 8
Ring (i.e., commutative ring with identity) 7
Ring of integers in a number field 82
Ring, Artinian 65 78
Ring, homomorphism and morphism of affine schemes 30
Ring, length of 66
Ring, local 51 65
Ring, map of 30
Ring, multiplicity of 66
Ring, Noetherian 26 67 172
Ring, spectrum of 9
Ringed space 21 22
Rings and affine schemes 36
Samuel, Pierre 125
Saturation 101
Scheme 28 230 231
Scheme as a set 9
Scheme as a topological space 10
Scheme of flexes 152
Scheme of left ideals 206
Scheme, affine 7 8 21 30
Scheme, arithmetic 81 110 162 180 185 188 245 249
Scheme, associated 68
Scheme, associated to vector space 105
Scheme, containment of schemes 23
Scheme, curvilinear 65
Scheme, degree of 62 65
Scheme, dimension of -s 27
Scheme, discriminant 231
Scheme, Family of schemes 70
Scheme, Fano 120 193—205 266 273
Scheme, finite 62
Scheme, Fitting 220
Scheme, general definition of 21
Scheme, group 258
Scheme, Hilbert 120 129 266
Scheme, irreducible 25
Scheme, length of 66
Scheme, local 50
Scheme, multiplicity of 65 66
Scheme, Noetherian 26 28 183 210
Scheme, nonaffine 22 33
Scheme, nonreduced 57 180
Scheme, nonsingular 28
Scheme, over 5 40
Scheme, over something 39 40
Scheme, primary 68
Scheme, projective 91 95
Scheme, reduced 25 47 53 68
Scheme, regular 28
Scheme, relative 35
Scheme, representable 252
Schemes: The language of modern algebraic geometry 4
Section 117
Section global 12
Section of 13
Section of a continuous map 13
Section of sheaf over open set 12
Segre, Beniamino 205
Segre, embedding 103 188
Segre, map 266
Separated 34 93
Separated scheme 34 93
Serre, Jean — Pierre 2 18 82 206
Set-theoretic image 209 222
Shafarevich, Igor R. 5 162
Sheaf in the Zariski topology 259
Sheaf of continuous functions 13
Sheaf of graded algebras 101
Sheaf of regular functions 9 11 19
Sheaf of regulars 9 11 19
Sheaf of sections 13
Sheaf, axiom 12 16
Sheaf, coherent 24 25
Sheaf, definition of 12
Sheaf, graded 118
Sheaf, ideal 24
Sheaf, invertible 112 116 117
Sheaf, normal 268
Sheaf, projectivization of 103
Sheaf, quasicoherent 24 25 40
Sheafification 16
Silverman, Joseph H. 275
singular 28 230 231
Singular, curve 155 242
Singular, point 230
Singularity 110 156 162 179 190 203 239 242 249 265 272 274
Small resolutions 179
Smith, Gregory 5
Smooth point 230
Smoothness 71
Space to Fano schemes 271
Space to Hilbert schemes 267
Space, affine 104 105
Space, projective 104 105
Space, Zariski 73 78 88 104 105 107 108 256 260 271
Spanier, Edwin H. 261
Spectrum 9
Spectrum of Noetherian ring 26
Spectrum of quotient ring 23
Stalk 13
Starr, Jason 5
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