360 INDEX Gabriel quiver, 61, 73, 74, see also McKay-Gabriel quiver Galois field extension, 63, 117–119, 330, 335, 337 Galois ring extension, 335–340 γ-invariant, 189, 190, 193–194 general linear group GL(n, k), 61, 62, 71, 78, 117, 335 generating invariants, 87–90, 152 generically Gorenstein, 177, 178, 184, 188, 189 genus, 25, 98 geometric McKay correspondence, 97–106 geometrically regular, 167 global dimension, 64, 78 gluing construction, 184, 194 gluing map, 248, 254, 257 going down, 17, 168, 326, 337 going up, 326, 337 golden ratio, 89, 96 Goldie dimension, 60 gonflement, 44, 170, 171–174, 281, 306, 314, 315 Gonzalez-Sprinberg, Gerardo, 97 Gorenstein generically, 177, 178, 184, 188, 189 in codimension one, 82, 150, 220, 262, 264, 312 on the punctured spectrum, 82, 116, 166, 196, 199, 206, 220, 262, 264, 313 Gorenstein dimension, 209 Gorenstein locus, 199 Gorenstein module, 179, 313 great gross 1728, 89 Green, Edward, 38, 41, 45, 49, 50 Greuel, Gert-Martin, 42, 50–52, 141, 145, 159, 160, 241, 245, 252, 284 Griffith, Phillip A., 311 group binary polyhedral, 86–90, 92–97, 151, 263 ´ etale fundamental, 117–119 fundamental, 117 Galois, 63, 119, 335 general linear, 61, 62, 71, 78, 117, 335 special linear, 81, 83, 86, 92, 151, 229 group algebra kG, 71, 268 Gulliksen, Tor, 151 Guralnick, Robert, 7, 199, 271 HT (R), 273 Harada-Sai Lemma, 268, 270, 275, 277, 278, 282 Harada-Sai sequence, 269, 269, 270, 276 Hashimoto, Mitsuyasu, 180, 182 Heitmann’s amazing theorem, 26, 307 Heitmann, Raymond C., 26 Heller, Alex, 31 Hensel’s Lemma, 6, 145, 146, 148 Henselian local ring, 6, 6, 7, 10, 48, 114, 118, 165, 181, 189, 210, 212, 217, 223–225, 228, 249, 272, 280, 317, 319 classical definition, 6, 145, 147, 317 complete local ring is, 6 Krull-Remak-Schmidt holds for, 6 Henselization, 163, 164, 165, 168, 169 Herzog, urgen, 81, 82, 90, 109, 116, 117, 119, 141, 150, 184, 189, 194, 195, 200, 262, 287, 293, 295, 298, 299 Hessel, Johann F. C., 84 Hessian, 89 higher direct image, 98 Higman, Donald G., 31, 272 Hilbert function, 58, 101, 160, 313 Hilbert polynomial, 58, 313 Hilbert-Burch Theorem, 288 Hom-tensor adjointness, 93, 221, 331 homogeneous coordinate ring, 25 homogeneous ring, 195, 287, 293, 294, 295 homological different, 274, 274, 285, 326–330, 336 homomorphism of matrix factorizations, 124, 127, 134 hosohedron, 84 hull of finite injective dimension, 175, 179, 179–194 Ext-minimal, 183 left minimal, 183
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