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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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Hodge filtration 317 Hole chart 66 Holomorphic, action 75 Holomorphic, embedding in 36 Holomorphic, function 21 Holomorphic, function is constant on a compact surface 29 Holomorphic, function of several variables 6 Holomorphic, function on an affine plane curve 22 Holomorphic, function, preserves orientation 5 Holomorphic, function, sheaf 270 Holomorphic, map 38 Holomorphic, map between tori 63 Holomorphic, map has discrete preimages 41 Holomorphic, map is an isomorphism if 1-1 40 Holomorphic, map is an isomorphism if degree one 48 Holomorphic, map to 166 Holomorphic, map to 153 Holomorphic, map to the Riemann Sphere 41 Holomorphic, map without coordinates 166 Holomorphic, map, 1-1 criterion 161 Holomorphic, map, branch divisor 134 Holomorphic, map, branch point 45 Holomorphic, map, defined by a linear system 160 Holomorphic, map, defined by monodromy 91 Holomorphic, map, degree 48 Holomorphic, map, degree of the image 164 Holomorphic, map, embedding 163 Holomorphic, map, embedding criterion 163 Holomorphic, map, hyperplane divisor 159 Holomorphic, map, inverse image divisor 133 Holomorphic, map, linear system of 156 Holomorphic, map, local normal form 44 Holomorphic, map, monodromy representation 87 Holomorphic, map, multiplicity 45 Holomorphic, map, ramification divisor 134 Holomorphic, map, ramification point 45 Holomorphic, map, the canonical map 203 Holomorphic, map, Veronese map 165 Holomorphic, one-form 105 106 Holomorphic, one-form on a hyperelliptic curve 193 Holomorphic, one-form on a projective plane curve 193 Holomorphic, one-form on a torus 193 Holomorphic, one-form, period of 248 Holomorphic, one-form, sheaf 271 Holomorphic, tangent vector field 341 Homogeneous coordinates 13 94 Homogeneous ideal 96 Homogeneous polynomial 14 31 Homomorphism of line bundles 334 Homomorphism of sheaves 278 Homotopic loops 84 Homotopy of paths 124 Hurwitz formula 52 135 244 Hurwitz’s theorem on automorphisms 82 Hyperelliptic involution 61 Hyperelliptic surface 61 92 167 Hyperelliptic surface and equality in Clifford 202 Hyperelliptic surface is an algebraic curve 170 Hyperelliptic surface, Abel — Jacobi fibers 264 Hyperelliptic surface, automorphisms 243 Hyperelliptic surface, function field 178 Hyperelliptic surface, homology generators 249 Hyperelliptic surface, meromorphic function on 62 Hyperelliptic surface, one-form on 193 Hyperelliptic surface, one-forms on 112 Hyperelliptic surface, the canonical map 204 Hyperelliptic surface, Weierstrass points and gap numbers 245 Hyperplane 96 Hyperplane, bitangent 220 Hyperplane, containing a divisor 208 Hyperplane, divisor 136 Hyperplane, divisor of a holomorphic map 159 Hyperplane, divisor, form the linear system 159 Hyperplane, divisor, monodromy of 222 Hyperplane, flexed 233 Hyperplane, general 221 Hyperplane, monodromy representation 222 Hyperplane, tangent 217 233 Hyperplane, transverse 218 219 Hypersurface 16 95 226 Hypersurface, containing the canonical curve 204 Identity Theorem 29 40 Implicit function theorem 10 Imposing conditions on hypersurfaces 226 Imposing independent conditions 226 Incidence space 212 Index of speciality 198 Infinitely near triple point 72 Inflection point 219 234 Inflection point, counting 241 Inflection point, Wronskian criterion 235 Inflectionary basis 234 Inflectionary weight 240 Initial point 118 Integral around a closed chain 248 Integral of a 1-form along a chain 121 Integral of a 1-form along a path 119 Integral of a 2-form 122 Integral of a trace 255 Integral, depends holomorphically on the end-points 198 Intersection divisor 136 Inverse image divisor 133 Inverse of an invertible sheaf 328 Invertible sheaf 324 Invertible sheaf is locally trivial 358 Invertible sheaf of a divisor 325 348 Invertible sheaf of sections of a line bundle 338 355 Invertible sheaf of tangent vector fields 341 356 367 Invertible sheaf, cocycle for 350 Invertible sheaf, extensions 362 Invertible sheaf, group 330 Invertible sheaf, inverse 328 Invertible sheaf, local generator 325 Invertible sheaf, tensor product 327 Invertible sheaf, trivialization 324 Irreducible polynomial 11 Isomorphism between 149 Isomorphism between 148 Isomorphism between L(D)’s 148 Isomorphism of covering spaces 85 Isomorphism of line bundles 334 Isomorphism of Riemann surfaces 40 Isomorphism of sheaves 287 Isotropy subgroup 75 Jacobian 248 264 319 356 K-plane 96 Kernel of a sheaf map 282 Kernel of an action 75 Lattice 9 43 Lattice in 263 Lattice, hexagonal 64 Lattice, homothetic to 44 Lattice, square 63 Laurent series 25 Laurent Series Approximation 173 Laurent tail 171 Laurent tail 1-form divisors 201 Laurent tail divisor 179 Line 8 18 57 96 241 Line bundle 333 Line bundle, atlas 333 Line bundle, automorphism 358 Line bundle, canonical bundle 337 339 Line bundle, chart 331 Line bundle, compatibility of charts 332 Line bundle, defined by transition functions 336 Line bundle, fiber coordinate 332 Line bundle, glueing 335 Line bundle, group 351 Line bundle, homomorphism 334 Line bundle, rational section 342 Line bundle, regular section 337 Line bundle, structure 333 Line bundle, support of a chart 331 Line bundle, tangent bundle 337 341 Line bundle, tautological 334 Line bundle, transition function 332 Line bundle, trivial 333 Line, flexed 266 Line, secant 99 Line, tangent 100 241 266 Line, transverse 266 Linear equivalence 138 Linear isomorphism of projective spaces 97 Linear subspace of 95 Linear system 147 Linear system of a holomorphic map 156 Linear system, base-point-free, free 157 Linear system, canonical 200 Linear system, complete 147 Linear system, defining a holomorphic map 160 Linear system, dimension 147 Linear system, fixed part/divisor 161 Linear system, gap number 233 Linear system, moving part 161 Linearly dependent subset of 96 Linearly independent subset of 96 Local complete intersection curve 18 37 205 Local generator for an invertible sheaf 325 Local Normal Form 44 Locally constant sheaf 273 Locally finite covering 299 Long Exact Sequence 298 299 Loop 84 Maximum modulus theorem 29 Meromorphic, function 24 Meromorphic, function , separating tangents 169 Meromorphic, function on 24 32 Meromorphic, function on a cyclic covering of the line 74 Meromorphic, function on a hyperelliptic curve 62 Meromorphic, function on a projective curve 25 36 37 Meromorphic, function on a torus 25 35 50 150 Meromorphic, function on an affine plane curve 36 Meromorphic, function on the Riemann Sphere 24 30 149 Meromorphic, function with poles bounded by D 146 Meromorphic, function with prescribed Laurent tails 173 Meromorphic, function with prescribed orders 173 Meromorphic, function, divisor of 130 Meromorphic, function, Laurent tail divisor of 179 Meromorphic, function, multiplicity one 169 Meromorphic, function, order 26 Meromorphic, function, separating points 169 Meromorphic, function, sheaf 271 Meromorphic, function, sum of the orders is zero 31 33 42 49 124 Meromorphic, function, trace 251 Meromorphic, n-fold differential 236 Meromorphic, one-form 106 107 Meromorphic, one-form on a cyclic covering of the line 112 Meromorphic, one-form on a hyperelliptic curve 112 Meromorphic, one-form on an affine plane curve 111 Meromorphic, one-form on an projective plane curve 112 Meromorphic, one-form on an projective plane curve with nodes 112 Meromorphic, one-form on the Riemann Sphere 111 Meromorphic, one-form with poles bounded by D 148 Meromorphic, one-form with prescribed Laurent tails 200 Meromorphic, one-form, divisor of 131 Meromorphic, one-form, order 107 Meromorphic, one-form, product 237 Meromorphic, one-form, pullback order formula 115 Meromorphic, one-form, ratio of two is a function 131 Meromorphic, one-form, residue 121 Meromorphic, one-form, sheaf 271 Meromorphic, one-form, sum of the residues is zero 123 Meromorphic, one-form, trace 252 Minimum of a set of divisors 136 Mittag-Leffler Problem 180 Moduli space for curves 215 367 Monodromy representation of a covering map 86 Monodromy representation of a holomorphic map 87 Monodromy representation of hyperplane divisors 222 Monodromy representation, defining a covering space 89 Monodromy representation, defining a holomorphic map 91 Monodromy representation, surjectivity 223 Monomial singularity 71 Moving part of a linear system 161 Multiplicity of a holomorphic map 45 Multiplicity of a holomorphic map and the order 47 Multiplicity of a holomorphic map, derivative formula 45 Multiplicity of a hyperplane meeting a projective curve 219 241 Multiplicity one function 169 Net 147 Node of a plane curve 67 102 144 Node of a plane curve, meromorphic one-form 112 Node of a plane curve, resolving 69 Nonsingular polynomial 11 Nonspecial divisors 210 Nullstellensatz 35 One-form of type (0,1) 110 One-form of type (1,0) 110 One-form, 109 One-form, 114 One-form, 114 One-form, closed 114 One-form, defined with an atlas 106 107 110 One-form, differential of 114 One-form, exact 113 One-form, holomorphic 105 106 One-form, integral along a chain 121 One-form, integral along a path 119 One-form, meromorphic 106 107 One-form, pullback 115 One-form, rational 309 One-form, rational with bounded poles 310 One-form, regular 310 One-form, residue 121 One-form, wedge product 113 Onto sheaf map 282 Open mapping theorem 40 Orbit 75 Order of a meromorphic 1-form 107 Order of a meromorphic function 26 Order of a meromorphic n-fold differential 237 Order of a rational section of a line bundle 343 Ordinary cusp 72 Ordinary plane curve singularity 72 Ordinary triple point 72 Orientable 6 Paracompact 299 Partition of a path 119 Partition of unity 302 Path 84 118 Path-connected 5 Path-lifting property 85 Pencil 147 Period 248 257 Period, mapping 126 Period, matrix 259 Picard group 263 345 Picard group and the Jacobian 356 Picard group as the group of invertible sheaves 348 Picard group as the group of line bundles 354 Picard group, isomorphic to 347 Plane curve, affine see “Affine plane curve” Plane curve, projective see “Projective plane curve” Plucker’s Formula 70 Plugging a hole 66 Poincare’s Lemma 117 284 306 Pole 23 Pole of a meromorphic 1-form 107 Pole of a meromorphic function 26
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