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| Brieskorn E., Knorrer H. — Plane Algebraic Curves |
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| Предметный указатель |
Euclidean algorithm (for Puiseux pairs) 514
Euclidean geometry I 117 I
Euclidean ring I 174
Euler characteristic of a curve 614
Euler characteristic of a fibre 550
Euler characteristic of a knot spanning surface 540
Euler characteristic of a singular fibre 603
Euler characteristic of a surface 609
Euler characteristic of the Miilnor fibre and the multiplicity sequence 569
Euler characteristic of the Milnor fibre and resolution graph 568
Euler's partial differential equation I 197
Exact p-form 635
Exceptional curve 463 470
Exceptional curve, of 1st kind 463
Exceptional hypersurface 470
Exceptional line 463
Exponent, first characteristic 484
Factorial ring (= UFD) I 174
Feynman integral 574
Fibration (of a knot) 543
Fibre see also Milnor fibre
Fibre bundle, locally trivial I 130
Fibre bundle, locally trivial differentiable 542
Fibre, 1st Betti number 550 573
Fibre, genus 544
Folium of Descartes I 88 I 590
Function germs, algebra 354
Function germs, holomorphic 330
Function germs, ring of holomorphic 330 354
Function germs, theorem on implicit 335 348
Function(s), doubly periodic I 313
Function(s), elliptic I 318
Function(s), holomorphic 329
Function(s), homogeneous I 194
Function(s), main theorem on symmetric 344
Function(s), ring of holomorphic 329
Function(s), transcendental I 79
Function(s), unfolding of 573
Function(s), Weierstrass  -, differential equation I 317
Function(s), Weierstrass -- I 303 I
Fundamental class I 264 I
Fundamental cycle I 269
Gauss — Manin connection 692
Gaussian hypergeometric series 687
General polynomial 342
Generation, organic (of curves) I 6
Genus arithmetic 610
Genus formula (for curves), generalised 624
Genus formula of Clebsch and Noether 601
Genus of a connected orientable surface 540
Genus of a knot 541
Genus of a surface 609
Genus of curves 324 576 596 603 610 614 619
Genus, Todd 611
Genus, virtual 613
Geometric monodromy group 664
Geometry of position I 106
Geometry, analytic I 66
Geometry, analytic, development of I 69
Geometry, complex-projective I 136
Geometry, Euclidean I 117 I
Geometry, projective I 90 I
Geometry, projective, development of I 102
Geometry, Riemannian I 119
Graph, dual 509
Grothendieck topology 335
Group, complex-projective-linear I 137
Group, Cremona 468
Group, real-projective-linear I 115 I
Harmonic mean point 591
Hensel's lemma 335
Henselian local ring 335
Henselisation 335
Hessian curve I 289
Hessian group I 297
Hessian matrix I 289
Hessian normal form of cubics I 293 655
Hexagon I 246
Hexagon and quadric I 246
Hilbert's basis theorem 345
Hilbert's Nullstellensatz I 192 352
Hodge decomposition 637 649
Holomorphic function 329
Holomorphic function s, ring of 329
Holomorphic function, germs 330
Holomorphic function, germs, algebra of 354
Holomorphic function, germs, ring of 330 354
Holonomy group (of a fibration) 664
Homogeneous coordinate system I 123
Homogeneous coordinates 456
Homogeneous equation I 117
Homogeneous function I 194
Homogeneous of degree n I 194
Homogeneous weighted I 195
Homogenisation I 117 I
Homology class I 262 I
Homology group I 260
Homology group of a projective algebraic subset I 273
Homology group of a submanifold I 272
Homology group,  singular I 263
Homology of Milnor fibre 573
Homology theory, singular I 263
Hopf, fibration I 138
Hopf, line bundle 461
Hopf, line bundle, complex, over  531
Horizontal family of cycles 665
Horizontal family of cycles, homology classes 665
Horizontal tangent space 663
Hurwitz formulae 613
Hurwitz formulae, generalised 626
Hyperbola I 5 I I I I
Hyperbola, projective equation I 117
Hyperboloid I 161
Hypercohomology, de Rham 637
Hypercohomology, de Rham, algebraic 639
Hypercohomology, de Rham, analytic 637
Hyperelliptic curve 620
Hypergeometric differential equation 686
Hypergeometric differential equation, monodromy group 687
Hypergeometric differential equation, series 687
Hyperplane I 123
Hypersurface 355
Hypersurface, affine algebraic I 191
Hypersurface, equation 355
Hypersurface, exceptional 470
Hypersurface, projective-algebraic I 199
Hypocycloid I 19
Hypocycloid, star curve, astroid I 32
Hypocycloid, three-cusped (Steiner's) I 32
Hypocycloid, three-cusped (Steiner's), polar 581
Hypotrochoid I 22
icosahedron I 266
Ideal, maximal 359
Ideal, maximal, of an analytic set germ 351
Implicit equation of a polynomial 334
Implicit function theorem 334 348
Index theorem of Atiyah — Singer 611
Infinitely near point 475 504
Infinitely near point,  -tuple 476
Infinitesimal calculus in geometry I 71
Inflection point of cubic I 284 I I
Inflection point, configuration (of cubics) I 295 I
Inflection point, improper I 288
Inflection point, number of 583
Inflection point, r-tuple I 288
integral I 71
Integral of 1st species 628
Integral of 2nd species 629
Integral of 3rd species 629
Integral, abelian 628
| Integral, elliptic I 318 656
Integral, Feynman 574
Integral, rectification I 86
Intersection class I 264
Intersection of curves I 90 I I
Intersection, complete 369
Intersection, cycle I 267 I
Intersection, multiplicity I 231
Intersection, multiplicity, of cycles I 269
Intersection, number, in the multiplicity sequence 512
Intersection, number, of curves I 238 I
Intersection, number, of cycles I 269 I
Intersection, number, of divisors 623 632
Intersection, ring I 260 I I
Intersection, theory I 90 I I
Invariant of curve, global 576
Invariant, j- I 302 I322 657
Invariant, order of curves I 88 I
Irreducible in integral domain I 173
Irreducible, component (of a set germ) 361
Irreducible, curve I 204
Irreducible, set germ 361
Isobaric I 195
Isolated singularity 359
Isomorphic, as algebraic manifolds I 313
Isomorphism, (mapping germ) 356
Isomorphism, birational 468
Isomorphism, Poincare 271
Jacobian variety 322
Kind of a differential form 628
Knot of singularity 535
Knot, fibred 542 543
Knot, genus 541
Knot, Neuwirth — Stallings 543
Knot, torus I 223
Krull, dimension 368
Krull, principal ideal theorem 369
Kummer configuration 586
Lattice (in  ) I 312
Legendre normal form (of cubics) 656
Lemniscate I 18
Length, proper (of a multiplicity sequence) 507
Leray coboundary 641 645
Line I 2 I I
Line at infinity I 114
Line bundle 460
Line bundle, canonical 624
Line bundle, complex (over  ) 531
Line bundle, Hopf 401
Line through a point 459
Line, complex-projective I 140
Line, equation I 72
Line, exceptional 463
Line, pencil I 240
Line, projective I 116
Linear system (of curves) I 240 615
Linear system (of curves) of cubics I 281
Linear system (of curves), dimension I 240
Linear system (of curves), given by a linear condition I 242
Linear transformation 455
Lissajou curves I 65
Lissajou curves, equation I 78
Local ring 328
Local ring, henselian 335
Localisation 328
Locally analytic 349
Locus I 3
Logarithmic pole (of a differential form) 642
Lojaziewicz trick 343
Main theorem of conformal mapping I 280
Main theorem on elementary symmetric functions 344
Malgrange trick 340
Malgrange, preparation theorem 345
Manifold, abelian I 313
Manifold, classification of compact orientable, 2-dim 324
Manifold, complex I 119
Manifold, complex, algebraic I 119
Manifold, development of concept 120
Manifold, differentiable I 119
Manifold, Jacobian 322
Manifold, n-dimensional topological I 118
Manifold, projective plane as I 118
Manifold, real algebraic I 119
Manifold, real algebraic, analytic I 119
Manifold, Riemannian I 119 .
Manifold, Stein 636
Mapping, germ 355
Mapping, main theorem of conformal I 280
Mapping, rational 468
Mapping, regular I 311
Maximal contact 481
Maximal contact, stability under blowing up 491
Maximal ideal 359
Mean point, harmonic 591
Metric, Riemannian I 119
Milnor fibration 544
Milnor fibration and Newton polygon 574
Milnor fibration in the standard resolution 561
Milnor fibration, 1st Betti number 550
Milnor fibration, homology 573
Milnor number 573
Modular surface, elliptic 661
Moduli I 322
Moduli space 322
Moduli space, dimension 322
Moebius band I 130 462 533
Monkey saddle 550
Monodromic 664
monodromy 691
Monodromy group 665
Monodromy group of a differential equation 687
Monodromy group of a fibration 665
Monodromy group of the hypergeometric equation 687
Monodromy group, geometric 664
Monodromy group, projective 679
Monodromy, geometric 574
Monodromy, theorem 692
Multiplicity at infinitely near points 598
Multiplicity of a curve at a point I 212 I
Multiplicity of cycles I 269
Multiplicity of intersection of two curves I 90 I
Multiplicity sequence 504
Multiplicity sequence and Puiseux expansion 512
Multiplicity sequence and resolution graph 521
Multiplicity sequence, proper length of 507
Multiplicity sequence, system 505
Neighbourhood in classical topology 329
Neighbourhood, formal, in ![$\mathbb{C}[[X_l,...,X_n]]$](/math_tex/ada1426a8130d49edbcc8737d6c3290582.gif) 336
Neighbourhood, germ 336
Neighbourhood, small 328
Neighbourhood, Zariski open 328
Neil's parabola see Parabola Neil's
Nephroid I 31
Neuwirth — Stallings knots 543
Newton polygon 370
Newton polygon and Milnor fibration 574
Nilpotent 354
Noether formula 614
Noether normalisation lemma 354
Noetherian ring 347
Non-orientability I 130
Normal crossings (of divisors) 498
Normal form, Weierstrass I 302
Nullstellensatz, Hilbert I 192 352
Nullstellensatz, Rueckert 351
octahedron I 266
One-sided surface (in space) I 130
Order (of a plane curve) I 88
Organic generation of conic sections I 6
Organic generation of the cissoid I 11
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