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



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
Maximum principle for subharmonic functions      55
Mean value property      52
Meromorphic function      196
Meromorphic function on a Riemann surface      158
Meromorphic map      243
Meromorphic section      201
Minimal defining function      194
Modification      236
Modification, generalized      236
Module      120
Moishezon manifold      320 353
Monic polynomial      113
Monoidal transformation      242
Monomial      9
Montel, theorem of      23
Nebenhulle      364
Negative line bundle      287
Neighborhood filter      100
Neil parabola      134
Neumann operator      359
Neumann problem      357
Noetherian      121
Normal bundle      182
Normal exhaustion      78
Normalized polynomial      113
Normally convergent      11
Nowhere dense.      37
Oka's principle      253
Oka, theorem of      100
Open covering      153
Open map      88
Orbit space      205
Order of a power series      119
Osgood space      243
Osgood, theorem of      19
Paracompact      153
Parameter system      151
Partially differentiable      16
Partition of unity      163
Pathwise connected      88
Period matrix      348
Picard group      187
Plucker embedding      218
Pluriharmonic function      318
Plurisubharmonic      56 261 263
Plurisubharmonic, strictly      59
Poincare map      301
Point of indeterminacy      196
Polar set      196
Pole      196
Poly normally convex      87
Polydisk      5
Polynomial      9
Positive definite      261
Positive divisor      198
Positive form      303
Positive line bundle      288
Power series, convergent      108
Power series, formal      11 105
Power sum      134
Prime element      117
Primitive polynomial      117
Principal divisor      254
Principal ideal domain      117
Projective algebraic manifold      217
Projective algebraic set      217
Projective space      208
Projective unitary transformations      318
Proper map      35 226
Properly discontinuous      205
Pseudoconvex      60 103
Pseudoconvex manifold      267
Pseudoconvex, strongly      73
Pseudodifferential metric      368
Pseudopolynomial      124
Pullback      see "Lifted bundle"
Pure-dimensional      143
Quadratic transformation      239
Quotient bundle      181
Quotient field      117
Quotient topology      203
Rational function      223
refinement      153
Refinement map      153
Region      6
Regular closure      245
Regular domain      360
Regular function      224
Regular point      39 140 161
Reinhardt domain      7
Reinhardt domain over $\mathbb{C}^{n}$      95
Reinhardt domain, complete      8 85
Reinhardt domain, proper      8
Remmert — Stein extension theorem      150
Removable boundary point      102
Removable singularity      196
Resolution of singularities      240
Riemann domain with distinguished point      89
Riemann domain, branched      229
Riemann extension theorem, first      38
Riemann extension theorem, second      151
Riemann surface of $\sqrt{z}$      88
Riemann surface, abstract      157
Riemann surface, concrete      230
Riickert basis theorem      122
Ritt's lemma      151
Runge domain      87
Saturated set      203
Scalar product      3
Schlicht domain      90
Schwartz, theorem of      285
Second axiom of countability      153
Section      see "Cross section"
Section in a fiber bundle      186
Segre map      225
Self-intersection number      241
Seminegative line bundle      352
Seminorm      284
Semipositive line bundle      352
Serre duality      233
Serre problem      259
Shear      109
Siegel upper halfplane      352
Singular cochain      189
Singular cohomology group      189
Singular homology group      189
Singular locus      147
Singular point      39
Singular q-chain      188
Singular q-simplex      188
Smooth boundary      64
Smoothing Lemma      59
Sobolev norm, tangential      358
Sobolev space      358
Standard simplex      188
Star      283
Stein manifold      251
Stiefel manifold      212
Stiitzflache      275
Stokes's theorem      305
Strict transform      240
Strictly pseudoconvex manifold      267
Strongly pseudoconvex      267
Structure group      173
Subbundle      180
Subelliptic      358
Subharmonic function      53
Submanifold      41 161
Submersion      168
Symbol of a differential operator      336
Symmetric polynomial      126
Tangent bundle      176
Tangent bundle of projective space      222
Tangent space      32 165
Tangent space, holomorphic      66
Tangent vector      32 165
Tangential map      167
Tautological bundle      238
Tensor power      178
Tensor product      179 261
Theorem A      252
Theorem B      253
Topological map      41
Topological quotient      203
Toric closure      246
Toric variety      246
Torsion point      230
Torus      207 225 348
Transformation group      172
Transition functions      173
Transversal      171
Trivial vector bundle      177
Trivialization      173
Trivialization of a vector bundle      175
Tube      288
Tube domain      87
Unbranched point      133
Uniformization      88 162
Union of Riemann domains      94
Unique factorization domain      117
Vector bundle      175
Vector bundle chart      175
Vector bundle homomorphism      177
Vector field      176
Veronese map      224
Volume element      323
Weakly holortiorphic      16
Wedge product      297
Weierstrass condition      113
Weierstrass division formula      115
Weierstrass formula      110
Weierstrass function      226
Weierstrass polynomial      114
Weierstrass preparation theorem      116
Weierstrass, theorem of      19
Whitney sum      177
Worm domain      366
Zariski tangential space      152
Zariski topology      141
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте