Index Abhyankar, 12, 28, 42, 45, 130, 131, 153, 157, 158, 160 Abramovich, 9 Albanese, 55 approximate manifold, 106 Atiyah, viii Bierstone, 61 Bravo, 61 Cano, 13 Chevalley, 24 Cohen, 22 completion of the square, 24 Cossart, 131 curve, 2 de Jong, 61, 131 derivations Hasse-Schmidt, 171 higher, 171 Eisenbud, viii Encinas, 61 exceptional divisor, 20, 39, 40 exceptional locus, 39, 40 Giraud, 70 Harris, viii Hartshorne, viii, 2 Hauser, 13, 61, 132 Heinzer, 13, 157 Hensel's Lemma, 23 Hironaka, 2, 15, 61, 62, 130 hypersurface, 2 intersection reduced set-theoretic, 62 scheme-theoretic, 2, 62 isolated subgroup, 134 Jung, 55 Karu, 9 Kawasaki, 11 Kuhlmann, 13 Levi, 55 Lipman, 130 local uniformization, 12, 130, 138, 147, 156 Macaulayfication, 11 Macdonald, viii MacLane, 137 Matsuki, 9 maximal contact formal curve, 28 formal hypersurface, 177 hypersurface, 56, 67, 70, 131, 177 Milman, 61 Moh, 61 monoidal transform, 16, 39, 40 monomialization, 13, 157 morphism birational, 9 monomial, 14 proper, 9 multiplicity, 3, 19, 25, 175 Nagata, 11 Narasimhan, 131 Newton, 1, 3, 6, 12 185
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