Index
A{ (kl = affine line), 79
AJ[ ( k2 = affine plane), 80
Ank ( kn = affine fl-space), 80, 83, 84
Abel, 158, 194,239
abelian group, 75
Abel's Theorem, 239
Abhyankar (S. K.), 208
Abhyankar (S. S.), 121, 153, 237, 239, 253
Abhyankar's inversion formula, 189
abstract algebra, 75, 79
addition, 75
addition process, 92, 93
additive abelian group, 75, 85, 245
additive subgroup, 77
adic expansion, 182-184
ADJW (set of all homogeneous adjoint
polynomials of degree m ), 150-152
adjoint, 150-152
adjoint condition, 151
adjoint polynomial, 150
AF + BG argument (Noether's
Fundamental Theorem), 147, 208
affine, 12-13
affine chart, 212
affine coordinate, 13
affine coordinate ring (of a plane curve;
usually k[x,y])y 65, 100, 105
affine coordinate ring (of a surface; usually
k[x,y,z])t 72
affine coordinate ring (of a variety; usually
AT[JC, , ...,*„]) , 105, 106,249
affine plane, 12, 41, 42-44, 46
affine ring, 101, 252
affine 3-space, 43
algebra, 25, 28, 31-32, 126
algebraic, 25, 27, 28
algebraic closure, 80, 180
algebraic criterion, 225
algebraic curve, 31, 45, 107, 136
algebraic dependence, 79
algebraic equation, 25
algebraic formula (for inversion), 193
algebraic function, 11,31
algebraic function field, 101, 113, 241, 246,
251-253
algebraic genus formula, 58, 59
algebraic geometry, 19-21, 25, 31, 81, 157,
249
algebraic hypersurface, 142
algebraic independence, 79
algebraic number, 31, 107
algebraic over, 79
algebraic plane curve, 108, 131, 136, 137,
141, 143, 145
algebraic variety, 82, 105-107, 244, 246,
249
algebraically, 24, 25, 26
algebraically closed, 70, 75, 83, 88, 99, 119,
125,246,248,250
algebraically dependent, 79
algebraically equivalent, 175
algebraically independent, 79
almost nonsingular, 212
ambient space, 129
ambient variety, 129
analysis, 32, 46, 87, 126, 208, 244
analysis way, 249
analytic approach, 240
analytic at, 69
analytic coordinate change, 127, 136, 207
analytic curve, 136
analytic decomposition, 136
analytic geometry, 3, 25
analytic hypersurface, 128
analytic irreducibility, 138, 141
analytic (plane) curve, 108, 126, 137, 141
analytic reducibility locus, 205
analytically unramified, 142
analyzing singularities, 236
antisymmetry, 245
aphorism, 18, 65, 123, 170, 208
approximate Z)th root of F ( \/T )y 182
arc, 247, 248
283
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