364 INDEX normal bundle, 100, 101 normal domain, 23–25, 63, 67, 81, 82, 98, 101, 104, 106, 117–119, 229, 230, 233, 234, 245, 246, 288, 291, 295, 306, 307, 311, 313, 325–331, 334, 336 normal forms, 89, 90, 146, 159–160 normal scheme, 117 number of generators, 297 O, 86 octahedron, 84 Odenthal, Charles, 17 ωR, 176 one-one correspondence, 61, 70–73, 83, 97, 105 orbit-stabilizer theorem, 338 orthonormal basis, 85 overring, 299 perfect field, 52, 141, 173, 267, 268, 275, 276, 279 periodic free resolution, 126 Peskine, Christian, 176 Picard group Pic, 25, 105 Piepmeyer, Greg, 203, 210 pitchfork construction, 184, 208 Platonic solids, 84, 86 point at infinity, 85 pointed ´ etale neighborhood, 164, 165, 319 Popescu, Dorin, 280 poset, 27 positive characteristic, 90, 99, 119, 146, 176 positive normal affine semigroup, see Krull monoid Prill, David, 69, 335, 339 prime avoidance, 285, 337 countable, 241, 242 primelike, 3 primitive element theorem, 38, 39, 283 principal ideal domain, 41, 42, 45, 47 principal ideal ring, 29, 30, 38, 39, 46, 55, 56, 294, 317 projective line, 85, 99, 102, 103 projective module, 20, 32, 43, 44, 46, 47, 56, 61, 64, 65, 70–73, 78, 83, 177, 230, 238, 249, 250, 306, 311, 323, 325, 328–330 projective plane, 102 projective space, 143 pseudo-reflection, 69, 69, 70, 72, 78, 79, 83, 107, 230, 335 pullback, 20, 42, 43, 48, 110, 111, 196, 197, 223, 234, 245, 246, 251, 252, 255, 257, 258 pure homomorphism, 110, 239 submodule, 110, 120, 239 pure height one, 177, 178, 188, 326, 327, 329, 330 pure local ring, 118 purely transcendental extension, 170 purity of the branch locus, 118, 326–334 pushout, 110–114, 127, 185–187, 219, 238 quasi-homogeneous polynomial, 89, 99, 192 quotient field, 63, 77, 98, 117, 118 rad and rad2, 224, 229, 239 ramification, 19, 66, 69, 321, 335, 337 ramification index, 338, 339 rank, 13, 20, 20, 22, 56, 69, 126, 176, 177, 179, 184, 189, 190, 234, 249, 268, 295, 296, 305, 313, 316, 332, 334 rational curve, 99 rational double point, see Kleinian singularity rational singularity, 98–101, 104, 119, 120, 151 Raynaud, Michel, 178 real numbers R, 79, 128 reduced matrix factorization, 125, 126, 131, 141 reduced ring, 38, 41, 45, 53, 172, 245, 246, 248, 259, 264, 268, 279, 299, 302, 305, 310, 316, 324, 325 reduced semigroup, 14 reduced syzygy redsyz, 219–223, 235, 289, 292, 296, 311 reduction, 101, 314 reflecting hyperplane, 335, 337
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