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Fritzsche K., Grauert H. — From Holomorphic Functions To Complex Manifolds
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Название: From Holomorphic Functions To Complex ManifoldsАвторы: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 392Добавлена в каталог: 20.11.2009Операции: Положить на полку |
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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 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 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
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