Okonek C., Schneider M., Spindler H. — Vector Bundles on Complex Projective Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Okonek C., Schneider M., Spindler H. — Vector Bundles on Complex Projective Spaces

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Название: Vector Bundles on Complex Projective Spaces

Авторы: Okonek C., Schneider M., Spindler H.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 414

Добавлена в каталог: 12.03.2005

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Предметный указатель

$\alpha$ -invariant      pp.114
$\alpha$ -invariant of a holomorpfaic 2-bundle over $\mathbb{P}_3$       115
Atiyah, M.F.      128 129 371
Barth, W.      45 88 228 234 320 367 369 370
Base-change theorem      11
Beilinson, relative version of the theorem of      306
Beilinson, theorem I of      240
Beilinson, theorem II of      245
Birkhoff, G.D.      44
Bogomolov, F.A., unstable in the sense of      190
Bott formula      8
Bundle      see vector bundle
Canonical bundle of a projective-algebraic complex manifold      7
Canonical bundle over $\mathbb{P}_n$       7
Cartan formula      14
Cartan — Eilenberg resolution      243
Cartier divisor      see divisor
Chern class      pp.12
Chern class Chern class of a line bundle      13
Chern class of $\mathbb{P}_n$       17
Chern class of an arbitrary vector bundle      14
Chern class of the hyperplane bundle      14
Chern class, first, of a torsion-free coherent sheaf      160
Chern class, total      14
Chern polynomial of a continous r-bundle over $\mathbb{P}_n$       112
Coherence theorem      10
Cohomology ring, singular, of $\mathbb{P}$       12
Conormal bundle of a Cartier divisor on a complex manifold      4
Conormal bundle of a locally complete intersection in $\mathbb{P}_n$       91
Conormal bundle of the zero locus of a section      91
Dedekind, R.      44
Degree of a divisor      5
Degree of homogeneity of a vector bundle      63
Descente lemma      195
Determinant bundle of a torsion-free coherent sheaf      154
Discriminant of a 2-bundle over I»      168
Divisor, Cartier      3
Divisor, effective      3
Dual class of a r-codimensional submanifold in. a complex manifold      20
Elencwajg, G.      46 70 71 74 235 237 370
Ellingsrud, G.      368
Endomorphism, regular      332
Euler characteristic      359
Euler sequence      6
Euler sequence, relative      305
Exponential sequence      18
Extension of line bundles      29
Extension, maximal normal, of a subsheaf in a reflexive sheaf      159
Extension, normal, of a subsheaf in a reflexive sheaf      157
Family of stable r-bundles      272
Ferrand, D.      269 .
Forster, O.      46 237
Fundamental class of $\mathbb{P}_n$       12
Geyer, W.D.      44
Gieseker semi-stable      173 see
Gieseker stable torsion-free coherent sheaf      173 see
Gieseker, D.      139 173 191 366 368
Grauert — Muelich theorem      206
Grauert, H.      44
Grothendieck, A., theorem of      22
Harder — Narasimhan-filtration      pp.60
Hartshorne, R.      89 110 370
Hartshorne, R., theorem of      343
Hilbert polynomial      272
Hilbert, D.      44
Hirschowitz, A.      70 71
Holomorphic structures on topological bundles      pp.111 117 122 128 130
Homogeneous holomorphic r-bundle      see vector bundle
Homological codimension      140
Homological dimension      139
Horrocks, G.      39 45 109 128 240 270
Horrocks, G., splitting criterion of      39
Horrocks, G., theorem of      39
Hulek, K.      45 236 332 367 369
Hulek, K., theorem of      332
Hulsbergen, W.      369
Hyperdirect image of a complex      243
Hyperplane bundle over $\mathbb{P}_n$       4
Indecomposable r-bundle      see vector bundle
Instanton bundle, complex, of rank 2      370
Instanton bundle, real, of rank 2      37
Jump line      pp.26
Jump line of second kind      236
Jump line, set of      29
k-homogeneous bundle      see vector bundle
Koszul complex of a section in a 2-bundle      92
Kronecker module, stable, of rank 2      321
Kronecker module, symmetric stable      350
le Potier      273 367 368
Line bundle is simple      75
Line bundle is stable      164
Line bundle, tautological, over $\mathbb{P}_n$       4
Local fundamental isomorphism      96
Locally complete intersection      pp.90
Lower term sequence      95
Maruyama, M.      139 177 228 272 320 366 367
Moduli of stable 2-bundles      pp.271
Moduli space      pp.271
Moduli space, $M_{\mathbb{P}_23(0,1)$       364
Moduli space, $M_{\mathbb{P}_2}(-1,-2)$       344
Moduli space, $M_{\mathbb{P}_2}(-1,n)$ is a fine moduli space      319
Moduli space, $M_{\mathbb{P}_2}(0,2)$       350
Moduli space, $M_{\mathbb{P}_2}(0,n)$ is a coarse moduli space      306
Moduli space, $M_{\mathbb{P}_2}(0,n)$ is a fine moduli space for n odd      311
Moduli space, $M_{\mathbb{P}_2}(0,n)$ is irreducible      320
Moduli space, coarse      274
Moduli space, construction of $M_{\mathbb{P}_2}(-1,n)$       pp.313
Moduli space, construction of $M_{\mathbb{P}_2}(o,n)$       pp.275

Moduli space, construction of the, for stable 2-bundles on $\mathbb{P}_2, M_{\mathbb{P}_2}(c_1,c_2)$       pp.271
Moduli space, fine      273
Monad      pp.238
Monad over a compact complex manifold      239
Monad, canonically associated to a stable bundle      307
Monad, cohomology bundle of a self dual      282
Monad, cohomology of      239
Monad, display of      239
Mumford, D.      109 160 189 270
Nakayama-Lemma      3
Normal sheaf      see sheaf
Null correlation bundle is simple      pp.77
Null correlation bundle, Chern classes of the      80
Null correlation bundle, is stable      180
Null correlation bundle, Moduli space of the, over JP-      364
Null correlation bundle, over $\mathbb{P}_n$ , n odd      pp.76
Plemelj, J.      44
Postnikov tower      115
Projection formula      12
Projective bundle, associated to a vector bundle      13
r-bundle      see vector bundle :
Rank of a coherent analytic sheaf      145
Rees, E.      128 129 137
Reflexive sheaf      149 see
Remmert, R.      44
Sato, E.      70 71 89
Schwarzenberger, R.L.E.      44 71 112 117 168 191 357
Schwarzenberger, R.L.E., condition of      113
Semicontinuity theorem      10
Semistability      see semi-stable sheaf and semi-stable vector bundle
Serre duality      7
Serre duality, Theorem A of      9
Serre duality, Theorem B of      10
Serre, J.P.      81 98 110
Seshadri, C.S.      44
Sheaf of ideals of a Cartier divisor      4
Sheaf, determinant bundle of a torsion-free coherent      154
Sheaf, first Chern class of a torsion-free coherent      160
Sheaf, generated by global sections      9
Sheaf, Gieseker semi-stable      173
Sheaf, Gieseker stable      173
Sheaf, k-th syzygy      145
Sheaf, normal coherent      150
Sheaf, normalized torsion-free      165
Sheaf, reflexive      149
Sheaf, semi-stable, over $\mathbb{P}_n$       160
Sheaf, stable, over $\mathbb{P}_n$       161
Sheaf, torsion-free coherent      147
Simple bundle      74 see
Singularity set of a coherent analytic sheaf      144
Singularity set of the homological codimension of a coherent analytic sheaf      144
Smith, L.      137
Spindler, H.      235
Splitting criterion of Horrocks      39
Splitting of vector bundles      pp.21
Splitting principle      15
Splitting type of a bundle on a line in $\mathbb{P}_n$       27
Splitting type of the tangent bundle over $\mathbb{P}_n$       27
Splitting type, generic      29
Stability      see stable sheaf and stable vector bundle
Stable vector bundle      161 see
Standard construction      pp.46
Standard diagramm      48
Strjzfrnme, S.A.      368
Syzygy sheaf      145 see
Syzygy theorem      140
Takemoto, F.      160 189
Tangent bundle is homogeneous      28
Tangent bundle is indecomposable      74
Tangent bundle is simple      74
Tangent bundle is stable      181
Tangent bundle is uniform      27
Tangent bundle, Chern classes of      17
Tangent bundle, holomorphic, of $\mathbb{P}_n$       6
Tango, H.      81 88
Tautological 2-bundle over G      47
Tautological line bundle over the associated projective bundle      4
Theorem A      9
Theorem B      10
Tjurin, A.N.      89
Torsion-free sheaf      147 see
Uniform bundle      27 see
Universal local deformation of a bundle      311
Van de Ven,A.      70 88 211 234
Vector bundle, associated to a locally complete intersection      pp.90
Vector bundle, canonical, over IP      7
Vector bundle, Gieseker semi-stable      173
Vector bundle, Gieseker semi-stable is semistable      174
Vector bundle, Gieseker stable      173
Vector bundle, Gieseker stable is simple      174
Vector bundle, homogeneous      28
Vector bundle, indecomposable      74
Vector bundle, indecomposable of rank (n-1) over $\mathbb{P}_n$       73
Vector bundle, k-homogeneous      62
Vector bundle, non homogeneous uniform of rank 3n-1      pp.62
Vector bundle, semi-stable      161
Vector bundle, simple      74
Vector bundle, simple of rank n-1 over $\mathbb{P}_n$       81
Vector bundle, stable      161
Vector bundle, stable is Gieseker stable      174
Vector bundle, stable is simple      172
Vector bundle, uniform      27
Vector bundle, uniform of rank r over $\mathbb{P}$ , r<n      pp.51
Vector bundle, unstable in the sense of Bogomolov      190
Vogelaar, J-.A.      130 131 135
Ward, R.S.      371
Weber, H.      44
Yang — Mills fields      371 .
Zero locus of a section in a bundle      91

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