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| Lewis J.D. — CRM Monograph Series, vol.10: A Survey of the Hodge Conjecture |
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| Предметный указатель |
Jacobian, generalized intermediate 236
Jacobian, higher 348
Jacobian, intermediate 343
Jacobian, intermediate, Griffiths 171
Jacobian, intermediate, Weil 171
Jacobian, Lieberman 173
Kaehler form 32
Kaehler manifold 11 29 32
Kaehler manifold, test 34
Kaehler metric 11 32
Kodaira dimension 266
Kodaira — Serre duality 60
Koszul complex 130
Kuenneth formula 161
L(G) (space of left-invariant derivations on G) 302
Lefschetz (1,1) theorem 58 79
Lefschetz (1,1) theorem, analog for Stein manifolds 67
Lefschetz decomposition 166 275
Lefschetz decomposition theorem 165
Lefschetz group 316 326 328 330 344 347
Lefschetz hyperplane section 71
Lefschetz pairing 167
Lefschetz pencil 71 227
Lefschetz theorem, strong (hard) 165 167 227 268 283 290
Lefschetz theorem, strong (hard), for Chow groups 275
Lefschetz theorem, weak 166 167
Lefschetz theorem, weak, for Chow groups 239
Lefschetz theorem, weak, for hypersurfaces 270
Lefschetz vanishing cocycle 206
Lefschetz vanishing cone 74 228
Lefschetz vanishing cycle 72 74 206 228
Leray cohomology sheaf 113 228
Leray spectral sequence 113 228 231
Level 265
Level of a Chow group 272 277 288
Level of a Hodge structure 265 272 345
Lf(A) (Lefschetz group of Abelian variety A) 316
Lie algebra 301 304 315
Lie algebra of an algebraic group 302
Lie algebra, bracket 301
Lie algebra, reductive 344
Lie algebra, semisimple part 344
Lie group 314
Lie group, compact 3
Lie group, complex analytic 3
Lie group, connected 3
Lie(G) (Lie algebra of algebraic group G) 302
Line bundle 20
Line bundle, (weakly) negative 22
Line bundle, (weakly) positive 22
Line bundle, ample 23
Line bundle, associated to a divisor 49
Line bundle, Chern class 33 46
Line bundle, metric on 32
Line bundle, positive 23 33
Line bundle, tautological 21 112
Line bundle, very ample 23
Linear algebraic group 298
Linear equivalence 49 83 84
Linear system 23 83
Lines, Fano variety 201
Local invariant cycle property 229
Local monodromy transformation 73 206 229 241
Local ring 48
Local trivialization 17
Lsogenous 316
Lsogeny 306 316 320
Lsogeny, degree of 306
Lsogeny, dual 306
Manifold 1—13
Manifold, flag 91
Manifold, Grassmannian 12
Manifold, Hermitian 24
Manifold, Hodge 12
Manifold, Hopf 13 34
Manifold, Kaehler 11 29 32
Manifold, Moishezon 11 15
Manifold, projective algebraic 11
Manifold, Riemannian 24
Manifold, Stein 8 9 66
Maximal order 305
Meromorphic form 50 76 129
Meromorphic form, Poincare residue 50 76 131
Meromorphic function field 11 36
Meromorphic map 200
Metric connection 106 116
Metric on a complex vector bundle 24
MHS (mixed Hodge structure) 241
Mixed Hodge structure 241 284 292
Mixed Hodge structure, extension 292
Moishezon manifold 11 15
Monodromy group 206
Monodromy theorem 241
Monodromy transformation see also “Local monodromy transformation”
MT(A) (Mumford — Tate group of Abelian variety A) 312
mt(V) (Lie algebra of MT(V)) 312
MT(V) (Mumford — Tate group of rational Hodge structure V) 312
Mumford — Serre conjecture 349
Mumford — Tate group 312 313—317 328 332 333 337
Mumford — Tate group, special 312
Mumford’s CM fourfold 333
Mumford’s example 333
Mumford’s theorem 252
N(Y/X) (normal bundle of Y in X) 42
Node 9
Noether — Lefschetz theorem 207
Non-singular point 8
Non-singular variety 10
Normal bundle 42
Normal function 76 236
Normal function, homology class 77 237
Normal function, horizontal 236
Normal function, main theorem 237 240
Numerical equivalence 273 274
Ordinary double point 71 80
Orientation, standard 34
Parseval’s Inequality 147
Period 5 75 178
Pg(X) (geometric genus) 41
Picard group 45
Picard group, continuous part 46
Picard variety 46
Picard — Lefschetz formula 73
Picard — Lefschetz transformation see also “Local monodromy transformation”
Pie(X) (Picard group) 45
Pluecker embedding 13
Pluricanonical differential form 254
Pohlmann’s criterion 337
Pohlmann’s theorem 338
Poincare divisor 84
Poincare duality 60
Poincare lemma 31
Poincare’s complete reducibility theorem 183 250 305 348
Poincare’s existence theorem 80 238
Polarization 12 14 97 313 314 316 321 324 349
Polarization, principal polarization 14
Positive involution 306
Presheaf 34
Presheaf, associated sheaf 35
Presheaf, complete 35
Primitive cohomology 123 128 134 166 193 211
Primitive homology 74 228
Principal torus 174
Privileged extension 235
Projection formula 111 189 257 286 290
Projective algebraic manifold 11
Projective bundle 111
Projective space 7
Projective space, canonical bundle 41
Projective space, cohomology 8
| Projective space, Picard group 63
Projective variety 10
Proper transform 190 243
Prym variety, generalized 343
q(X) (irregularity of X) 83
QM-type 309
Quadratic transform see also “Blow-up”
Quartic threefold, Hodge conjecture 209
Quartic threefold, uniruledness 98 213
Quasi-decomposable 320
Quaternion algebra 304 330
Quaternion algebra, canonical involution 304
Quaternion algebra, definite 304 324 325
Quaternion algebra, Hamiltonian 304 307 345
Quaternion algebra, indefinite 304 325
Quaternion algebra, maximal order 305
Quaternion algebra, order 305
Quaternion algebra, partially indefinite 336
Quaternion algebra, reduced norm 304
Quaternion algebra, reduced trace 304
Quaternionic multiplication 309 330 343
Rank of a vector bundle 17
rank(K,S) (rank of CM-type) 337
Rational algebraic cohomology class 63
Rational curve 3
Rational equivalence 49 83 194
Rational form 129
Rational function field 8
Rational map 200
rdim A (reduced dimension of A) 331
Real multiplication 308 329
Real multiplication, generalized 329
Reduced dimension 331
Regular map 182
Regularity theorem 151 154
rel dim(A) (relative dimension of A) 333
Relative dimension 333 335
Rellich lemma 148 151
Representation 300 313
Representation, contragredient 300
Representation, dual 300
Representation, G-equivariant 300
Representation, G-linear 300
Representation, half-spin 304 315
Representation, irreducible 300
Representation, odd 341
Representation, reductive 313
Representation, semisimple 313
Representation, spin 303 304 315
Representation, standard 300 315 346
Representation, subrepresentation 300
Representation, symplectic 315
Res (residue) 127
Residue 76 127
Residue map, generalized 86
Restriction of scalars functor 299 300
Riemann form 305 306 309 314 327 349
Riemann form, equivalent 306
Riemann — Roch theorem see also “Hirzebruch — Riemann — Roch theorem”
Riemannian manifold 24
Riemannian metric 24
Rigidity 336
RM-type 329
Rosati involution 307 323
Sheaf 35
Sheaf of invariant cocycles 229
Sheaf, coherent 9 51
Sheaf, cohomology 37
Sheaf, exact sequence 37
Sheaf, fine 37
Sheaf, invertible 51
Sheaf, locally free 51
Sheaf, resolution 38
Sheaf, torsionless 38
Siegel half-space 310 335 343
Similtude norm 301
Simple Abelian fourfold 323
Simple abelian variety 326
Singular homology 60
Singular point 9 (see also “Double point”)
Skyscraper sheaf 37 110 127
SL(n) (special linear group of size n) 301
Smooth base locus 228
Smooth cubic 125
Smooth hypersurface 92
Smooth point see also “Non-singular point”
SO(n) (special orthogonal group in n variables) 301
SO(V,S) (special orthogonal group on V with respect to symmetric form S) 301
Sobolev lemma 147 151
Sobolev Norm 147
Sobolev s-norm 146 151
Sobolev s-space 146
Sp(2n) (symplectic group in 2n variables) 301
Sp(V,E) (symplectic group on V with respect to symplectic form E) 301
Special orthogonal group 332
Special unitary group 301
Sporadic cycle 338
Standard conjectures, Grothendieck’s 349
Standard Lefschetz conjecture 259
Standard Lefschetz conjecture for Abelian variety 259
Standard Lefschetz conjecture for complete intersection 259
Standard Lefschetz conjecture for flag manifold 259
Standard orientation 34
Standard representation 318 324 332 346 347
Star operator 139 141 145 349
Stein manifold 9 66
Stein manifold, Theorem A 66
Stein manifold, Theorem B 67
Stoke’s theorem for analytic varieties 61
SU(n):=SU(n,0) (special unitary group on n variables) 301
SU(p,q) (special unitary group of signature p, q) 301
SU(V,H) (special unitary group on V with respect to Hermitian form H) 301
Sub-Hodge structure rational 346 347
Sub-Hodge structure rational, irreducible 347
supp (support) 37
Symmetric group 340
Symmetric product 75 247
Symplectic group 301 332 345
Symplectic group, semisimple 301
Symplectic representation 323 324 332 335 336
Symplectic similitude group 301
Symplectic space 303
T(X) (real tangent bundle) 18
T*(X) (real cotangent bundle) 18
Tangent bundle 18 29
Tangent space 8 302
Tate conjecture 348 349
td(V), td(X) (Todd class) 119
Todd class 119
Torsion algebraic cocycle 68
Torsion class 9 60
Total transform 189 243
Totally indefinite division quaternion algebra 326
Totally real algebraic number field 307
Totally real field 323 325—327
Transition functions 2 17
Triangular polymer without double bond 337
Triangular polymer without Hexatram 337
Triangular polymer without short cycle 337
Type H 330
Type of Abelian variety 307
U(k,n) (universal bundle) 18
U(n) (unitary group) 13 301
U(p,q) (unitary group of signature p, q) 301
U(V,H) (unitary group on V with respect to Hermitian form H) 301
Uniformization 9
Unimodular 175
Unirational variety 92 94 200
Unirational variety, Hodge conjecture 92 200
Uniruled variety 92 214
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