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| Brieskorn E., Knorrer H. — Plane Algebraic Curves |
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| Предметный указатель |
Organic generation of the conchoids I 15
Orientability I 130
OUTLINE I 41 I I I
p-boundary I 262
p-chain I 261
p-cycle I 262
p-cycle, bounding I 260
p-form with logarithmic pole 642
p-form, closed 635
p-form, exact 635
p-form, rational on  646
parabola I 4 I I I
Parabola, diverging I 92 I
Parabola, generalized I 87 I I
Parabola, Neil's (= semicubical) I 87 I I I I I I I 473 496
Parabola, Neil's (= semicubical), rectification I 87
Parabola, projective equation I 118
Parallel, curve I 41
Parallel, curve, of a parabola I 55
Parallel, projection I 104
Parametrisation, rational (of curves) I 77 I
Pascal configuration I 248
Pascal theorem I 247
Pasting of disc bundles 533
Pasting, topological I 153
Pencil, linear (of curves) I 240
Pericycloid I 19
Period of a differential form 628
Period, relations (Riemann) I 321
Period, residual 629
Peritrochoid I 24
Perspectivity I 11
Plane, complex projective see projective n-dim space
Plane, dual projective I 251
Plane, real projective I 114
Platonic solids I 266
Pluecker formulat 576 584
Plumbing 533
Poincare isomorphism I 271
Poincare, duality theorem I 270
Point at infinity I 90 I
Point,  -tuple infinitely near 476
Point, infinitely near 475 504
Point, multiplicity at infinitely near 598
Point, ordinary n-tuple I 225
Point, regular I 213 363 686
Point, singular I 213 363 686
polar 592
Polar  588
Polar coordinates I 78
Polar description 589
Polar in a circle 578
Polar of a curve 587
Polar of a curve relative to a point 588
Polar of a family of curves 592
Polar, general 594
Pole (of a differential equation) 642
Pole-polar relationship 578
Polygon, Newton 477
Polyhedra, regular I 266
Polynomial I 172
Polynomial as implicit equation 334
Polynomial ring I 174
Polynomial, adjoint 601
Polynomial, associated I 200
Polynomial, division I 174
Polynomial, general 342
Polynomial, homogeneous I 194
Polynomial, homogeneous, weighted I 195
Polynomial, primitive I 176
Polynomial, Weierstrass 338
Position, general I 243
Position, special I 243
Power series, ring of convergent 331
Power series, ring of formal 331
Power series, ring of formal, neighbourhood 336
Preimage, proper 470
Preimage, strict 470
Preimage, total (of the standard resolution) 529
Preparation theorem, Malgrange 345
Preparation theorem, Weierstrass 338
Prime element I 173
Prime ideal chain 368
Principal congruence subgroup 679
Principal divisor (of a function) I 313
Principal ideal theorem, Krull 369
Projection, centre of I 102
Projection, stereographic I 142
Projective algebraic hypersurface I 199
Projective algebraic hypersurface, subset I 139
Projective geometry I 116
Projective line I 116
Projective line, complex I 140
Projective linear group, complex I 137
Projective linear group, real I 123
Projective linear subspace I 123
Projective monodromy group 679
Projective plane, real I 114
Projective properties (Poncelet I 106)
Projective space 459
Projective space, complex n-dimensional I 136 I
Projective space, complex n-dimensional, intersection ring I 260
Projective space, real n-dimensional I 122
Projective subspace, linear I 123 I
Projective viewpoint I 102
Projectively related figures I 111
Projectivity I 113
Puiseux chain 522
Puiseux pairs I 214
Puiseux pairs and multiplicity sequence 512
Puiseux pairs and resolution graph 522
Pure-dimensional (set germ) 367
Quadratic transformation 455 498
Quadrature (of the circle) I 3 I
Quadric I 91 I I I I 455 619
Quadric and hexagon I 246 I
Quadric, projective I 142
Quartic I 207 455
Quasihomogeneous see Weighted homogeneous
Quintic I 207
Radical (of an ideal) 351 354
Rational mapping 468
Rectification (of curves) I 86
Reduced algebra 354
Reducible set germ 361
Regular I 82
Regular curve I 79
Regular mapping (of algebraic manifolds) I 311
Regular point I 213 363
Regular polyhedron I 266
Regular singular point 686
Regularity theorem 692
Relatively prime I 175
Remainder (in polynomial division) I 174
Representative (of a set germ) 350
Residual period 629
Residue 641
Residue theorem 644
Resolution and Puiseux expansion 522
Resolution by quadratic transformations 455 496
Resolution graph 503 506
Resolution graph, contractible 529
Resolution of singularities 323 325 366 503
Resolution, standard 498
Resolution, topology of 531
Resultant (of polynomials) 178 196 202
Resultant (of polynomials), computation of intersection of curves 230
Riemann connectivity 610
Riemann period relations I 321
Riemann sphere I 141
| Riemann surface I 119 I 564
Riemann surface of a function I 155
Riemann surface, abstract I 156
Riemann surface, concrete I 156
Riemann surface, covering the sphere I 153
Riemann — Roch theorem 611
Riemannian geometry I 119
Riemannian manifold I 119
Riemannian metric I 119
Ring of convergent power series 331
Ring of entire algebraic functions 333
Ring of formal power series 331
Ring of holomorphic function germs 330 354
Ring of holomorphic functions 329
Ring of rational functions in Zariski neighbourhoods 328 311
Ring, algebraic local 328
Ring, local 328
Ring, local, henselian 335
Ring, Noetherian 345
Ring, spectrum of 332
Rotation reciprocator I 33 I
Rouche's theorem 353
Rueckert basis theorem 345
Rueckert Nullstellensatz 351
Schemes 332
Segre embedding 500
Seifert circles 537 551
Self-intersection number (of zero section of line bundle) 531
Set germ, analytic 349
Set germ, analytic, ideal 351
Set germ, decomposition 361
Set germ, morphisms 357
Set germ, representative 350
Set, affine-algebraic 191
Set, analytic 337
Sextic I 207
Sheets (of a covering) I 152
Shell curve (Ddrer) (see also Conchoid) I 47
simplex I 260
Simplex, singular I 263
Singular homology group I 263
Singular homology group, theory I 263
Singular point I 81 I I I 363
Singular point (on outline) I 52
Singular simplex I 263
Singularity, isolated I 10 I 350
Singularity, resolution of 359
Singularity, set 323 366
Solid, platonic I 266
Space, algebraic 337
Space, projective 459
Species (= kind) of a differential form 628
Species (= kind) of integral of a differential form 628
Spectrum (of a ring) 332
Sphere, covering of I 153
Sphere, Riemann I 141
Spider lines I 24
Spiric sections (of Perseus) I 16 I
Stallings, Neuwirth — Stallings knots 543
Standard resolution 498
Star (of a point in a triangulation) I 266
Stein manifold 636
Strata 366
Stratification 366
Structure, algebraic (of a curve) I 203
Structure, differentiable I 119
Study's lemma I 192
Subdivision, barycentric I 265
Submanifold, homology class of a I 272
Subset, analytic 349
Subset, complex-analytic I 139
Subset, projective-algebraic I 139
Subset, topological I 140
Subspace, projective linear I 123 I
surface see projective curve
Surface, elliptic 660
Surface, one-sided, in space I 130
Swallowtail I 188
System (of multiplicity sequences) 505
t-general 338
t-regular 338
Tangent equation I 80
Tangent problem I 71 I I
Tangent space, horizontal 663
Tangent space, vertical 663
Tangent to a curve I 213 I
Tautochrone I 29
tetrahedron I 266
Tetrahedron group I 299
Theorem, Artin approximation 336
Theorem, Atiyah — Singer 611
Theorem, Bertini 617
Theorem, Bezout I 227 I I
Theorem, Brianchon I 256
Theorem, Chow I 140
Theorem, Enriques — Chisini 516
Theorem, Liouville I 314
Theorem, M.Noether 518
Theorem, Milnor 543
Theorem, Pascal I 247
Theorem, Poincare duality I 270
Theorem, Riemann — Roch 611
Theorem, Rolle I 286
Theorem, Rouche 353
Theorem, Seifert 536
Theorem, Torelli I 322
Todd genus 611
Topology of resolution 531
Topology, classical 3289
Topology, Etale 33
Topology, Grothendieck 335
Toroid I 41
Torus, complex I 313
Torus, equation I 76
Torus, higher-dimensional I 320
Torus, knot I 223 544
Torus, knot, as braid 551
Transformation, birational 468
Transformation, Cremona 468
Transformation, group, Cremona 468
Transformation, linear 455
Transformation, quadratic 455 496
Transformation, Tschirnhaus I 182
Triangular coordinates I 108 456
Triangulation I 260
Trick of Lojaziewicz 343
Trick of Malgrange 340
Triple point I 213
Trisection of angle I 3 I I
Trochoid I 21
Trochoid, rotation-reciprocator I 33 I
Tschirnhaus transformation I 182
Tubular neighbourhood I 132
UFD (= factorial ring) I 174
Unfolding (of a holomorphic function) 573
Vanishing cycle I 162
Vanishing line I 105
Vanishing point I 105
Variety I 191
Variety, abelian I 306
Vertical tangent space 663
Virtual genus 613
Wankel motor I 38
Watt curves I 58
Wave front (of a parabola) I 55
Weierstrass  -function I 303 I
Weierstrass -function, differential equation I 317
Weierstrass dimension 368
Weierstrass formula 339
Weierstrass normal form I 302
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