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