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| Brieskorn E., Knorrer H. — Plane Algebraic Curves |
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| Предметный указатель |
 -Process 462 491
-process, n-dimensional 464
Abelian integral 628
Addition on cubics 306
Adjoint curve 598
Adjoint polynomial 601
Algebra of holomorphic function germs 354
Algebra, application in geometry I 69
Algebra, reduced 354
Algebraic curve I 79 I
Algebraic cycle I 274
Algebraic de Rham theorem 639
Algebraic local ring 328
Algebraic manifold I 119
Algebraic space 337
Algebraic structure I 203
Algorithm, euclidean (for Puiseux expansion) 514
Analysis and synthesis I 66
Analytic set 337
Analytic set germ 349
Analytic set germ ideal 351
Analytic set, at a point 348
Analytic set, locally 349
Analytic subset 349
Angle trisection I 3 I I
Arithmetic genus 610
Artin approximation theorem 336
Astroid I 32
Astroid equation I 81 I
Astroid genus 619
Astroid natural equation I 86
Astroid polar 582
Astroid Puecker formulae 585
Astroid singular points I 81
Barycentric calculus I 110
Barycentric subdivision I 265
Base point (of a linear system) 615
Basis theorem, Hilbert 345
Basis theorem, Rueckert 345
Bertini theorems 617
Betti number I 270
Betti number of a fibre 550 573
Bezout's theorem I 270 I I I
Birational isomorphism 468
Birational transformation 468
Birational transformation group 468
Blowing up a point 462
Boundary (of a chain) I 262
Bouquet (of topological spaces) I 143
Brachistochrone I 27
Braid (torus knots) 551
Branch of a set germ 361
Branch of the multiplicity sequence 504
Branch, point (of a covering) I 147
Brianchon's theorem I 256
Bundle of vector spaces 460
Bundle, Hopf 461
Bundle, line 460
Canonical divisor 622
Canonical line bundle 622
Cardano formula I 68 I
Cardioid I 30
Cartier divisor 622
Cassini curves I 18 I
Catacaustic I 31
Catastrophe I 53
Catastrophe theory I 53
Caustic I 31
Caustic of a parabola I 55
Caustic, stable I 55
Cell, chain, of a triangulation I 266
Cell, decomposition, dual I 264
Central projection I 102
Chain, cell- I 266
Chain, closed I 261
Chain, p- I 261
Characteristic, exponent, first 484
Characteristic, term of the Puiseux expansion 411
Chern class 623
Chern class, numbers 611
Chevalley dimension 368
Chow ring I 275
Chow theorem I 140
circle I 3
Circle equation I 73 I I I
Circle, evolute I 19
Circle, quadrature I 3 I
Circle, Seifert 537 551
Cissoid (of Diocles) I 9 I
Cissoid (of Diocles), equation I 74
Cissoid (of Diocles), polar 579
Class of a curve I 254 576
Class, Chern 623
Class, intersection (in homology theory) I 268
Classification of compact orientable, 2-manifolds 324
Classification of cubics I 87 I
Classification of curves I 87 I 323
Classification of quadrics I 278
Classification of singularities 323
Clebsch formula 619
Closed chain I 261
Closed p-form 635
Coboundary, Leray 641
Coherent sheaf 360
Cohomology class 653
Cohomology, de Rham 635
Cohomology, de Rham, group 635
Collinear points I 243
Collineation I 111 I I I
Collineation, homogeneity of polynomials preserved under I 204
Complete intersection 369
Completion of a curve I 207
Completion of the affine plane I 113
Complex, simplicial I 260
Conchoid of Nicomedes I 13
Conchoid of Nicomedes, equation I 75
Condition, linear (in a linear system) I 242
Configuration of a quartic 586
Configuration of lines on a cubic surface 586
Configuration, Desargues' I 248
Configuration, Kummer's 586
Configuration, Pascal's I 248
Configuration, tactical I 296
Conformal mapping, main theorem I 280
Conic section I 4 I
Conic section, general equation I 74
Conic section, organic generation I 6
Conjugation (as a mapping) I 137
Connection, Ehresmann 663
Connection, Gauss — Manin 692
Connectivity, Riemann 610
Contact, exponent 484
Contact, maximal 481
Contact, maximal, stability under blowing up 491
Continuity principle (of Poncelet) I 136
Contour (caustic) I 41
Contraction of graphs 529
Coordinates, affine I 124 I
Coordinates, Cartesian I 106
Coordinates, development of I 66
Coordinates, exchange I 116 I
Coordinates, homogeneous I 110 I I 456
Coordinates, local I 119
Coordinates, neighbourhood I 119
Coordinates, system, homogeneous I 123
Coordinates, triangular I 108
Covering, branched I 147 I
Covering, branched, of Riemann sphere I 154
Cremona group 468
Cremona transformation 468
| Cross ratio I 106
Crossing, normal (of divisors) 498
Cube, cell decomposition I 266
Cube, duplication of I 3 I I
Cubic I 87 I I I 689
Cubic as abelian variety I 308
Cubic as topological space I 163
Cubic classification I 304
Cubic cohomology 684
Cubic genus 619
Cubic Hesse normal form I 293 655
Cubic Legendre normal form 656
Cubic Plueer formulae 584
Curve as complex analytic subset I 139
Curve as topological subset I 140
Curve in the complex projective plane I 139
Curve in the projective plane I 117
Curve with multiple components I 239
Curve, abstract I 203
Curve, algebraic I 79 I
Curve, algebraic, affine I 172 I I
Curve, algebraic, projective I 203
Curve, algebraic, projective, complex I 203
Curve, Cassini I 18 I
Curve, class I 254
Curve, classification I 88
Curve, complete I 203
Curve, complex I 139
Curve, complex, projective I 203
Curve, defined by a differential equation I 79
Curve, dual I 86 I 576
Curve, elliptic I 319 324
Curve, embedding in a space I 219
Curve, equation I 71 I
Curve, exceptional 463 470
Curve, genus 324
Curve, geometric (Descartes) I 79
Curve, Hessian I 289
Curve, hyperelliptic 620
Curve, intersection number I 238
Curve, irreducible I 204
Curve, Lissajou I 65
Curve, order I 88 I
Curve, pencil I 240
Curve, plane I 202
Curve, plane, algebraic I 203
Curve, plane, complex algebraic I 203
Curve, rational I 280
Curve, transcendental I 79
Curve, Watt I 58
Cusp (of a curve) I i0
Cycle, algebraic I 274
Cycle, bounding I 260
Cycle, fundamental I 269
Cycle, horizontal family 665
Cycle, intersection I 267 I
Cycle, p- I 260 I
Cycle, vanishing I 162
Cycloid I 20
Cycloid, equation I 78
Cycloidal gear I 33
Cycloidal pendulum I 30
de Rham algebraic theorem 639
De Rham cohomology group 635
de Rham hypercohomology 637
de Rham theorem 636
Decomposition (of a set germ) 361
Deformation of a curve 620
Deformation of a singularity 366
Degree of a curve I 207
Degree of a polynomial I 174 I
Degree, n, homogeneous I 194
Delian problem I 3 I I
Derivative I 71
Desargues' configuration I 248
Desargues' theorem I 248
Descartes, folium of I 88 I 589
Dialectic (in mathematics) I 66 I
Diffeomorphism I 126
Differentiable structure I 119
Differential equation, hypergeometric 686
Differential equation, monodromy 687
Differential form and cohomology 635
Differential form on a curve 634 654
Differential form on a Riemann surface 627
Differential form, (p,q) 637
Differential form, 1st species 628
Differential form, 1st species, (on a curve) 649
Differential form, 2nd species 629
Differential form, 3rd species 629
Differential form, closed 635
Differential form, exact 635
Differential form, holomorphic 628
Differential form, meromorphic 628
Differential form, rational 638
Dimension of a set germ 367
Dimension of an analytic subset 367
Dimension, Chevalley 368
Dimension, Krull 368
Dimension, Weierstrass 368
Disappearing line (in central projection) I 105
Discriminant I 181 I
Discriminant of polynomials of degree 3 and 4 I 182
Division algorithm, euclidean I 174
Division theorem (for convergent power series) 339
Division theorem (for convergent power series), special 340
Divisor of a function (principal divisor) I 313
Divisor of a singular curve 529
Divisor on the projective plane I 240
Divisor, canonical 624
Divisor, Cartier 622
Divisor, common (of polynomials) I 177
Divisor, greatest common I 175
Divisor, intersection number of 623
Divisor, Weil 622
dodecahedron I 266
Double point (of a curve) I 213
Dual cell decomposition I 264
Dual curve I 86
Dual curve (polar) 576
Dual graph 509
Dual projective plane I 251
Dualisation I 251
Duality principle I 252 I
Duplication (of the cube) I 3 I I
Ehresmann connection 663
Elementary chain (of a resolution graph) 522
Elementary symmetric functions, main theorem on 344
Elimination (in equations) I 179
ellipse I 4 I
Ellipse, parallel curves of I 41
Ellipsograph I 8
Elliptic curve I 306 I 324
Elliptic function I 318
Elliptic integral I 318 656
Elliptic modular surface 661
Embedding, Segre 500
Envelope I 31 I
Epicycles I 19
Epicyclic curves I 19 I
Epicycloid I 19
Epitrochoid I 23
Equation from a parametrisation I 180
Equation of a curve I 206
Equation of a hypersurface 355
Equation of a polynomial, implicit 334
Equation, affine I 207
Essential term of Puiseux expansion 411
Etale topology 335
Euclidean algorithm I 174
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