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Miranda R. — Graduate studies in mathematics (vol.5). Algebraic curves and Riemann surfaces
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Название: Graduate studies in mathematics (vol.5). Algebraic curves and Riemann surfacesАвтор: Miranda R. Аннотация: This text is an introduction to the theory of algebraic curves defined over the complex numbers. It begins with the definitions and first properties of Riemann surfaces, with special
Язык: Рубрика: Математика /Алгебра /Алгебраическая геометрия /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1995Количество страниц: 390Добавлена в каталог: 23.03.2005Операции: Положить на полку |
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Pole of a meromorphic function is isolated 29 Presheaf 269 Presheaf, constant 271 Principal divisor 130 Principal part 181 Projection 98 Projective algebraic set 95 Projective curve 36 Projective line 8 Projective line has no deformations 367 Projective line, automorphism 43 Projective line, holomorphic map to, defined by monodromy 91 Projective line, isomorphic to the Riemann Sphere 40 Projective line, meromorphic function 24 32 Projective linePole of a meromorphic n-fold differential 238 Projective n-space 16 94 Projective n-space, dual 166 Projective n-space, holomorphic embedding in 36 Projective n-space, holomorphic map to 153 Projective plane 13 Projective plane curve 14 Projectively normal 231 Projectivization of a vector space 94 147 166 Properly discontinuous action 83 Pullback of a 1-form 115 Pullback of a divisor 134 Pullback of a path 254 Ramification divisor 134 Ramification point 45\ Rational function field see “Function field” Rational normal curve 165 216 Rational normal curve has no inflection points 245 Rational normal curve is the canonical image of a hyperelliptic curve 204 Rational normal curve, achieves the Castelnuovo bound 229 Rational section of a line bundle 342 Rational section of a line bundle, divisor of 343 Rational section of a line bundle, order of 343 Refinement of a triangulation 51 Refinement of a triangulation, common refinements exist 51 Refinement of a triangulation, elementary 51 Refinement of an open covering 293 Refining map 293 Regular function 309 Regular, one-form 310 Regular, section of a line bundle 337 Regular, tangent vector field 341 356 Removable singularity 23 Reparametrization of a path 118 Residue 121 Residue map 188 Residue of a trace 253 Residue theorem 123 186 200 Residue Theorem, algebraic proof 253 Resolving a node 69 Restriction maps 116 269 Reversal of a path 118 Riemann bilinear relations 262 Riemann sphere 4 Riemann Sphere as a rational normal curve 165 Riemann Sphere has trivial Jacobian 248 Riemann Sphere is an algebraic curve 170 Riemann Sphere is the only curve of genus zero 197 Riemann Sphere, computation of L(D) 149 Riemann Sphere, finite groups acting on 80 Riemann Sphere, function field 177 Riemann Sphere, holomorphic maps to 41 Riemann Sphere, isomorphic to 40 Riemann Sphere, linear equivalence on 140 Riemann Sphere, meromorphic function on 24 30 Riemann Sphere, meromorphic one-form 111 Riemann surface 4 Riemann — Roch problem 186 Riemann — Roch problem, motivating Cech cohomology 290 Riemann — Roch theorem 186 192 Riemann — Roch Theorem, Geometric Form 208 Riemann — Roch Theorem, implies algebraicity 195 SCROLL 209 Secant line 99 Second countable 4 Section of a line bundle 337 Section of a presheaf 269 Section of the canonical bundle 339 Section of the tangent bundle 341 Section, global 269 Section, rational, of a line bundle 342 Separates points 169 Separates tangents 169 Serre duality 188 Sheaf 272 Sheaf of 270 Sheaf of 323 Sheaf of forms 271 Sheaf of harmonic functions 271 Sheaf of holomorphic functions 270 Sheaf of meromorphic functions 271 Sheaf of meromorphic functions with poles bounded by D 271 Sheaf of nonzero holomorphic functions 271 Sheaf of not identically zero meromorphic functions 271 Sheaf of rational 1-forms 310 Sheaf of rational functions 310 Sheaf of regular functions 309 Sheaf of regular one-forms 310 Sheaf, algebraic 309 Sheaf, axiom 272 Sheaf, constant 273 Sheaf, direct sum 277 Sheaf, homomorphism 278 Sheaf, invertible 324 Sheaf, isomorphism 287 Sheaf, locally constant 273 Sheaf, map 278 Sheaf, map, 1-1 282 Sheaf, map, induces a cochain map 291 Sheaf, map, induces a cohomology map 293 296 Sheaf, map, kernel 282 Sheaf, map, onto 282 Sheaf, map, short exact sequence 284 Sheaf, restriction to an open subset 276 Sheaf, skyscraper 273 Sheaf, stalk 277 Sheaf, totally discontinuous 273 Short exact sequence 181 Short exact sequence of sheaves 284 Simple plane curve singularities 72 Simple tangency 219 Simply connected 84 Singularity 23 Skyscraper sheaf 273 Small loop around a point 88 Small path enclosing a point 118 Smooth complete intersection curve 17 Smooth projective curve 36 Smooth projective plane curve 16 Span of a divisor 208 Special divisor 198 Stabilizer 75 Stalk 277 Standard identified polygon 247 Stoke’s Theorem 123 Subchart 1 Support of a divisor 129 Support of a function 302 Support of a line bundle chart 331 Tacnode 72 Tangent bundle 337 341 367 Tangent hyperplane 217 Tangent line 100 241 266 Tangent sheaf 329 Tangent vector field 341 Tautological line bundle 334 Tensor product of invertible sheaves 327 Theta-function 34 50 Totally discontinous sheaf 273 Trace of a 1-form 253 Trace of a function 251 Transform of a 109 Transform of a 2-form 111 Transform of a holomorphic 1-form 105 Transform of a meromorphic 1-form 106 Transform of a meromorphic n-fold differential 236 Transition function between charts 2 Transition function for line bundle charts 332 Transition function for line bundle charts for the canonical bundle 337 Transition function for line bundle charts for the tangent bundle 337 Transition function for line bundle charts, cocycle conditions 335 Transition function for line bundle charts, defining a line bundle 336 Transverse hyperplane 218 219 Transverse line 266 Triangulation 50 Trigonal algebraic curve 209 Triple point 72 Trivialization of an invertible sheaf 324 Twisted cubic curve 17 100 102 145 165 216 Two-form on a Riemann surface 111 Two-form, 110 Two-form, defined with an atlas 111 Two-form, integral 122 Two-form, pullback 115 Two-form, sheaf 271 Two-form, transform of 111 Universal cover 85 Universal cover of a compact Riemann surface with 83 Universal cover of a torus 62 Veronese map 165 204 Very ample divisor 163 195 Web 147 Wedge product 113 Weierstrass points 242 Zariski topology 95 311 Zero Mean Theorem 318 Zero of a meromorphic 1-form 107 Zero of a meromorphic function 26 Zero of a meromorphic function is isolated 29 Zero of a meromorphic n-fold differential 238
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