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Barth W., Peters C., Van de Ven A. — Compact complex surfaces
Barth W., Peters C., Van de Ven A. — Compact complex surfaces



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Название: Compact complex surfaces

Авторы: Barth W., Peters C., Van de Ven A.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 161

Добавлена в каталог: 12.03.2005

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Предметный указатель
$A_{n,g}$-singularity      see Singularity
$\sigma$-Process      27—28 59—61 78
A-D-E curves      74—78 90
Adjunction formula      22 48 68
Affine geometry      244—246
Affine geometry, linear map      244
Albanese map      35
Albanese map of a weight-1 Hodge structure      37
Albanese map, torus      35
Algebraic dimension      22 23
Algebraic dimension, fibre bundle      139
Algebraic dimension, index theorem      see lndex
Algebraic dimension, surface      128
Algebraic dimension, variety      44 128
Almost-complex structure      18 129—131
Almost-complex structure, surface      129—131 228
Almost-quaternionic structure      265
Ample line bundle      44 134
Ample line bundle, Nakai's criterion for      127
Ample line bundle, Orauert's criterion for      44 45
Analytic fibre      6 2
Analytic fibre bundle      139
Analytic inverse image      24
Analytic pull-back      24
Analytic restriction      26
Andreotti — Weil conjectures      4 288
Arithmetical genus      19
Arithmetical genus of an embedded curve      68 75
Artin's criterion for rational singularities      75
Barlet-topology      259
Barlow construction      236
Base change map      26
Base change property      96 98
Base change theorem of Grauert      26
Base points of a meromorphic map      113
Basis, canonical      12—13 37 101
Basis, normalised      38
Beauville construction      236
Bertini's theorem      45
Bimeromorphic correspondence      71
Bimeromorphic map      71 79
Bimeromorphic transformation      71 86
Bimeromorphically equivalent fibrations      91
Bimeromorphically equivalent surfaces      72
Blowing up      28
Bounded domain of type IV      282
Bounded domain, quotient of a      177 229
Branch point      41
Branching order      41
Bundle along the fibres      19
Bundle, ample line      44 134
Bundle, elliptic fibre      143—149
Bundle, higher germs      149
Bundle, hyperplane      9
Bundle, normal      18 47
Bundle, principal elliptic      143
Bundle, projective, of a vector bundle      17
Bundle, tangent      18 47
Bundle, tautological line      19
Bundle, very ample line      44
Burniat construction      235
C-isomorphism      215
Calabi's conjecture      4 39
Campedelli construction      234
Canonical (line) bundle      18
Canonical basis      see Basis
Canonical basis formula for elliptic fibrations      161—164
Canonical flag      23 216
Canonical map, 1-canonical map      227
Canonical map, m-canonical mp      114 206
Canonical model, abstract      216
Canonical model, m-canonical model      114 216
Castelnuovo's rationality criterion      2 190—192
Castelnuovo's second inequality      211
Chamber      242
Characteristic classes      17—18
Characteristic classes, Chem casses      17
Characteristic classes, Chern character      17
Characteristic classes, L-classes      17
Characteristic classes, Pontrjagin classes      17
Characteristic classes, Stiefel — Whitney classes      17
Characteristic classes, Todd class      17
Chern class      see Charactertic classes
Chern numbers      206 211 228—237
Chow's theorem      44
Classification of elliptic fibrations (without multiple fibres)      160
Classification, Enriques      2 190
Classification, Enriques Kodaira      3 6 187
Closed embedding      24
Comparison theorem of Grauert      27
Complete deformation      see Deformation
Complete intersection      137
Complex space      24—27
Complex surface      1
Cone, Kaehler      239 257
Cone, positive      238
Connected divisor      68
Connected divisor, 1-connected (numetlcally connected) divisor      69
Connected divisor, m-connected divisor      68—69
Connected divisor, sum of differentiable manifolds      129
Construction (of surfaces of general type), Barlow      236
Construction (of surfaces of general type), Beauville      236
Construction (of surfaces of general type), Burniat      235
Construction (of surfaces of general type), Campedelli      234
Construction (of surfaces of general type), Catanese      236
Construction (of surfaces of general type), Godenux      234
Construction (of surfaces of general type), Inoue      235
Contraction of exceptional curves      72
Correlation morphism      12
Covering branched (or ramified)      41
Covering branched at the coordinate axes      82
Covering tricks(branched and unbranched)      43
Covering, branch points of a      41
Covering, branching order of a      41
Covering, double      86—90 182—186 276—280
Covering, local degree of a      41
Covering, ramification points of a      41
Covering, unbranched (unramified or etale)      41
Covering,cyclic      42
Critical point      90
Critical value      90
Curvature, holomorphic sectional      40
Curve      25
Curve on a surface      47
Curve, (-1)-exceptional      72 74 78—80
Curve, (-2)-exceptional      73
Curve, (semi-)stable      93 94
Curve, A-D-E      72—74 90
Curve, exceptional      71—72 78—80
Curve, rational      142 see (-2)-curves
Curve, smooth      18
Cusp      178
Cyclic quotient      84—85
De Rham (cohomology) group      32
De Rham isomorphism      32
de Rham's theorem      32
Decomposition of bimeromorphic maps      79
Decomposition sequence      48
Deformation of $P_2$      136 202
Deformation of a compact complex manifold      29
Deformation of surfaces      121—123 202—205
Deformation, (locally) complete      30
Deformation, (locally) universal      30
Deformation, versal      30
Degree of a line bundle on a curve      50 see
Degree of a map      11
Degree of a vector bundle on a curve      50
Desingulatisation of curves on surfaces      60—61 see
Desingulatisation of surfaces      85—86
Desingulatisation, Kodaira      2 23 79—80 111 114 162—164 187
Desingulatisation, logarithmic Kodaira      218
Direct image shenves      10 96—97
Direct image shenves, Grauert's theorem on      26
Discriminant of a lattice      12
Divisor      22
Divisor, 1-connected      68—70
Divisor, effective (positive)      22
Divisor, exceptional      28
Divisor, linear equivalent      22
Divisor, nol-negative      22
Divisor, pluricanonical      218—220
Divisor, ramification      41
Divisor,m-connected      69
Divisorial classes      238
Divisorial classes, effective      238
Divisorial classes, indecomposable      238
Divisorial classes, irreducible      238
Divisorial classes, nodal      238
Dolbeault (cohomology) group      33 118
Dolbeault's isomorphism      33
Double covering      see Covering
Double point      62 see
Dualising sheaf      48
Dualising sheaf for a fibration      98
Duality      see Poincare duality relative Serre
Elementary transformation      201
Elliptic configuration      273
Elliptic fibration      149—167
Elliptic fibre bundle      143—149
Elliptic pencils on Enriques surfaces      272—275
Elliptic surface      2 6 149 194 197;
Elliptic, properly, surface      189 202
Enriques clarification      2 190
Enriques surface      2 6 184 189 240 270—288
Enriques surface, general      279
Enriques surface, non-special      275—277
Enriques surface, special      275
Enriques — Kodaira classification      3 6 187
Euler characteristic of a coherent sheaf      19
Euler characteristic, topological      18 97
Exceptional curve of a $\sigma$-process      78—80
Exceptional curve of a bimeromorphic map      71—72
Exceptional curve of the first kind      72 78—80
Exceptional divisor      28
Exceptional surface      254
Exponential cohomology sequence      21 36 49
Exponential function      9
Exponential map      49
Exponential sequence      21 49
Extension theorem of Levi      27
Extension theorem of Riemann      27
Factorisation lemma      79
Fake projective plane      5 136
Fake quadric      177
Family      see also Deformation
Family of compact complex manifolds      29
Family of elliptic curves      29
Family, base space of a      29
Family, locally trivial      29
Family, pull-back of a      29
Family, smoth      29
Fibration      90—112
Fibration, bimeromorphically equivalent      91
Fibration, elliptic      149—167
Fibration, jacobian      153—155
Fibration, Kodaira      167—169
Fibration, n-th root      92—93
Fibration, relatively minimal      92
Fibration, stable      93—96 151—153
Fibre bundle      see also Bundle
Fibre bundle, algebraic      139
Fibre bundle,analytic      139
Fibre, (semi-)stable      93—94
Fibre, analytic      26
Finiteness theorem of Cartan — Serre      26
Fixed part of a linear system      113
Froehlicher spectral sequence      33 117 134
Functional invariant of an elliptic fibration      151
Fundamental class      70
Fundamental cycle      76 77
Fundamental points      71
GAGA-theorems      44 113
Genus, arithmetic(al)      19 68
Genus, geometric      1 19 67
Gieseker scheme      206—208
Gieseker's theorem      206
Godenux construction      234
Godenux surface      170
Graph of type A-D-E, $\tilde{A}$-$\tilde{D}$-$\tilde{E}$      16
Grauert — Fisher's local triviality theorem      29
Grauert's amplehess criterion      44—45 126
Grauert's base-change theorem      26
Grauert's comparison theorem      27
Grauert's contraction criterion      72
Grauert's direct image theorem      26
Grauert's semi-continuity theorem      26
Halfpencil      273
Hermitian metric, standard      268
Hilbert modular surface      177-182
Hirzebruch surfaces      141 142 188
Hirzebruch — Atiyah — Singer Riemann — Roch theorem      20
Hirzebruch — Jung singularities      80 112
Hirzebruch — Jung strings      73—74 80—85
Hodge decomposition      34—35 118
Hodge filtration      33
Hodge isometry      238
Hodge manifold      45
Hodge metric      44
Hodge numbers of surfaces      123—125
Hodge structure of weight-1      36—37
Homological invariant of an elliptic fibration      159
Hopf surface      4 6 146 172—174 176
Horikawa's representation of Enfiques surface      277
Hotikawa surfaces      233
Hurwitz formula      41
Hyperbolic plane      14
Hyperelliptic surface      148 189
Ideal sheaf      24
Iitaka's conjecture $C_{1,2}$      109—112 190
Iitaka's conjecture $C_{m,n}$      5
Index of a manifold      18
Index of a quadratic form      14
Index of a sublattice      12
Index theorem of Thom — Hirzebruch (topological-theorem)      18
Index, algebraic, theorem (Hodge-theorem)      120
Inoue construction      235
Inoue surface      174—175
Inoue — Hirzebruch surface      176
Intersection multiplicity      65
Intersection number      66
Inverse image sheaf      24
Irreducible component      25
Irregularity      1 86
J-function      151
Jacobian fibration      153—155
K3-surface      2 3 189 238 240—269 288
Kaehler class      34
Kaehler cone      242 257—258
Kaehler form      34
Kaehler manifold      34—36 40 114
Kaehler surface      115
Kaehler-Einstein metric      39 266
Kodaira dimension      2 23
Kodaira fibration      167—169
Kodaira surfaces, primary      146 189
Kodaira surfaces, secondary      147 189
Kodaira — Spencer map      31
Kodaira's criterion for Hodge manifolds      45
Kodaira's table. of singular (elliptic) fibres      150
Kummer surfaces      170 246—250 252 256 288
1 2
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