Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Fritzsche K., Grauert H. — From Holomorphic Functions To Complex Manifolds
Fritzsche K., Grauert H. — From Holomorphic Functions To Complex Manifolds

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: From Holomorphic Functions To Complex Manifolds

Авторы: Fritzsche K., Grauert H.

Аннотация:

This book is an introduction to the theory of complex manifolds. The authors' intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example, the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable. The book can be used as a first introduction to several complex variables as well as a reference for the expert.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 392

Добавлена в каталог: 20.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$H_{n}$      108
$z_{1}$-regular      109
$\overline{\partial}$-Neumann conditions      357
1-complete      267
1-convex      267
Abel's lemma      12
Abelian variety      351
Absolute space      7
Accessible boundary point      101
Acyclic covering      185
Adjoint operator      330
Adjunction formula      215
Affine algebraic      217
Affine algebraic manifold      224
Affine algebraic set      224
Affine part      210
Algebraic derivative      125
Analytic disk      47 102
Analytic polyhedron      85
Analytic set      36 160
Analytic tangent      275
Analytically dependent      320
Antiholomorphic form      303
Antiholomorphic gradient      28
Ascoli, lemma of      23
Atlas      155
Automorphism      226
Ball      5
Banach algebra      105
Bergman kernel      370
Bergman metric      372
Bergman projection      370
Bertini, theorem of      225
Betti number      190
Biholomorphic      33 159
Blowup      237
boundary conditions      357
Boundary distance      54 58
Boundary function      64
Boundary operator      189
Bracket      332
Branch locus      227
Branch point      128
Branched covering      128 227
Branched domain      229
Bubble method      283
Canonical bundle      174
Caratheodory distance      371
Cartan — Thullen, theorem of      77
Cauchy integral      17
Cauchy — Riemann equations      29
Cech cohomology      185
Center of a modification      236
Chain rule      32
Chern class      256
Chow, Theorem of      217
Closed map      226
Closure of $\mathbb{C}^{n}$      245
Closure of a manifold      244
Coboundary      184 187
Coboundary operator      183
Cochain      183 187
Cocycle      183 187
Codimension      151
Cohomologous      174
Cohomology group      184 187
Commutator      332
Compact exhaustion      163
Compact map      see "Completely continuous"
Compactification, one-point      153
Compatibility condition      173
Compatible coordinate systems      154
Complete hull      24
completely continuous      285
Completely singular      49
Complex 1-form      261
Complex covariant r-tensor      261
Complex differentiable      14
Complex gradient      15
Complex manifold      155
Complex n-space      1
Complex structure      1 155
Complexification      2
Cone      216
Conical set      216
Conjugation      2
Connected      6 88
Continuity of roots      134
Continuity principle      47
Continuity theorem      43
Contractible space      189
Convergence, compact      12
Convergence, domain of      13
Convergent series of numbers      10
Convex      8 66 74
Convex hull      73
Convex, strictly      67
Coordinate system      154
Cousin-I distribution      253
Cousin-II distribution      254
Covariant tangent vector      261
Critical locus      227
Cross section      176
cuboid      276
Cuboid, distinguished      276
Current      328
Current, harmonic      336
de Rham group      311
de Rham isomophism      312
de Rham sequence      310
Decomposition theorem of Hodge — Kodaira      339
Defining function      64
Degree of a hypersurface      220
Derivation      33 164
Derivative of a holomorphic map      30
Derivative, directional      16
Derivative, partial      15
Derivative, real      26
Derivatives, Wirtinger      28
Diagonal      162
Differential      260 300
Differential form      297 300
DIMENSION      161
Dimension of a submanifold      39
Dimension of an analytic set      142
Dimension of an irreducible analytic set      141
Dimension, local      150
Dirichlet's principle      52
Discrete map      228
Discriminant      127
Discriminant set      128
Distinguished boundary      6
Divisor      198
Divisor of a meromorphic function      198
Divisor of a meromorphic section      201
Dolbeault group      311
Dolbeault sequence      310
Dolbeault's lemma      309
Dolbeault's theorem      312
Domain      6
Domain of Existence      97
Domain of holomorphy      49 99
Domain of holomorphy, weak      49
Dual bundle      178
Duality theorem of Poincare      337
Duality theorem of Serre — Kodaira      338
Effective divisor      see "Positive divisor"
Effective group operation      172
Elementary symmetric polynomial      126
Elliptic operator      337
Embedded-analytic irreducible component      135
Embedded-analytic set      135
Embedding      214
Embedding dimension      152
Embedding theorem      145 258
Energy form      359
Envelope of holomorphy      87 97
Equivalence of bundles      174
Equivalence of systems of transition functions      174
Euclidean coordinates      322
Euclidean Domain      125
Euler sequence      223
Exact sequence      223
Exceptional set      236
Exhaustion function      58
Exterior algebra      298
Exterior derivative      301
Factorial monoid      125
Faithful      see "Effective group operation"
Fefferman, theorem of      369
Fiber bundle      173
Fiber bundle isomorphism      174
Fiber metric      341
Fiber product      171
Filter basis      100
Finite map      227
Finite module      121
Fixed point      172
Form of type (p, q)      298
Frame      177 313
Frechet space      285
Frechet topology      285
Free group operation      172
Fubini metric      319
Fundamental form      315
Gauss's lemma      117
General linear group      172
Genus      232
Genus of a Riemann surface      340
Geodesic coordinates      316
Geometric series      11
Germ      123 192
Globally generated      176
Gluing      170
Gluing of fiber bundles      173
Gluing of manifolds      170
Godeaux surface      225
Good topological space      189
Graph      161
Graph of a meromorphic function      242
Grassmannian      212 225
Greatest common divisor      117
Griffiths negative      341
Griffiths positive      342
Harmonic form      335 356
Harmonic function      52
Hartogs convex      48 99
Hartogs figure, Euclidean      25
Hartogs figure, general      43 99
Hartogs triangle      365
Hartogs, theorem of      307
Hausdorff space      153
Hensel's lemma      120
Hermitian form      3 261 321
Hermitian metric      314
hessian      67
Hodge manifold      346
Hodge metric      346
Hodge star operator      323
Holder continuous      367
Holomorphic form      303
Holomorphic function      13 96 257
Holomorphic function on a complex manifold      156
Holomorphic function on an analytic set      134
Holomorphic gradient      28
Holomorphic map      30 158
Holomorphically convex      75 100 251
Holomorphically convex hull      75
Holomorphically separable      251
Holomorphically spreadable      251
Homogeneous      9
Homogeneous coordinates      209
Hopf bundle      238
Hopf manifold      208 225
Hopf's a-process      237
Hyperbolic manifold      368
Hyperelliptic involution      234
Hyperelliptic surface      232
Hyperplane at infinity      210
Hyperplane bundle      220 221
Hyperquadric      219
Hypersurface      127 220
Hypersurface, analytic      160
Ideal      108
Identity theorem for analytic sets      142
Identity theorem for holomorphic functions      22
Identity theorem for meromorphic functions      197
Identity theorem for power series      21
Identity theorem on manifolds      156
Immersion      168
Implicit function theorem      34
Incidence set      237
Indeterminacy, set of      243
Inner product, Euclidean      4
Inner product, Hermitian      3
Integral class      346
Integral domain      113
Inverse mapping theorem      33
Irreducible analytic set      141
Irreducible component      131
Irreducible element      117
Isomorphism of complex manifolds      159
Isomorphism of vector bundles      177
Jacobian, complex      30
Jacobian, real      31
Kahler manifold      316
Kahler metric      316
Kernel form      370
Kobayashi metric      368
Kodaira's embedding theorem      344
Krull topology      110
Kugelsatz      44 307
Laplacian      334
Leray covering      see "Acyclic covering"
Levi condition      66
Levi convex      66
Levi convex, strictly      66
Levi form      57 263
Levi's extension theorem      197
Levi's problem      51
Lie group      171
Lifted bundle      180
Lifting of a differential form      304
Limit of a filter      101
Line bundle      175
Line bundle, associated to a hypersurface      200
Line element      314
Linear subspace      218
Liouville theorem of      22
Local @-algebra      192
Local homeomorphism      88
Local parametrization      39 41
Local potential      318
Local uniformization      231
Locally compact      153
Locally finite covering      153
Logarithmically convex      83
Maximal ideal      108
Maximum principle      22
Maximum principle for plurisubharmonic functions      264
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте