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Rational singularities, with applications to algebraic surfaces and unique factorization. (English) Zbl 0181.48903

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[1] S. S. Abhyankar, On the valuations centered in a local domain,Amer. J. Math.,78 (1956), 321–348. · Zbl 0074.26301 · doi:10.2307/2372519
[2] —-, Resolution of singularities of arithmetical surfaces, pp. 111–152, inArithmetical Algebraic Geometry, New York, Harper and Row, 1965 (edited byO. F. G. Schlling).
[3] M. Artin, Some numerical criteria for contractability of curves on algebraic surfaces,Amer. J. Math.,84 (1962), 485–496. · Zbl 0105.14404 · doi:10.2307/2372985
[4] —-, On isolated rational singularities of surfaces,Amer. J. Math.,88 (1966), 129–136. · Zbl 0142.18602 · doi:10.2307/2373050
[5] N. Bourbaki, Algèbre commutative, chap. 5–6,Act. Sci. et Ind., no 1308, Paris, Humann, 1964. · Zbl 0205.34302
[6] E. Brieskorn, Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen,Math. Annalen,166 (1966), 76–102. · Zbl 0145.09402 · doi:10.1007/BF01361440
[7] —-, Rationale Singularitäten komplexer Flächen,Inventiones Math.,4 (1968), 336–358. · Zbl 0219.14003 · doi:10.1007/BF01425318
[8] P. du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I),Proc. Cambridge Phil. Soc.,30 (1934), 453–459. · JFM 60.0599.01 · doi:10.1017/S030500410001269X
[9] (cited [EGA...]),A. Grothendieck andJ. Dieudonné, Éléments de Géométrie algébrique,Publ. Math. Inst. Hautes Études Sci., no8 4, 8, ..., 32 (1960, ..., 1967).
[10] H. Hironaka, Desingularization of excellent surfaces,Advanced Science Seminar in Algebraic Geometry, Bowdoin College, Brunswick, Maine, 1967.
[11] –, Forthcoming paper on desingularization of excellent surfaces,J. Math. Kyoto Univ.
[12] S. Kleiman, Toward a numerical theory of ampleness,Ann. of Math.,84 (1966), 293–344. · Zbl 0146.17001 · doi:10.2307/1970447
[13] W. Krull, Beiträge zur Arithmetik kommutativer Integritätsbereiche,Math. Z.,41 (1936), 545–577. · JFM 62.1105.01 · doi:10.1007/BF01180441
[14] S. Lichtenbaum, Curves over discrete valuation rings,Amer. J. Math.,90 (1968), 380–405. · Zbl 0194.22101 · doi:10.2307/2373535
[15] H. T. Muhly andM. Sakuma, Some multiplicative properties of complete ideals,Trans. Amer. Math. Soc.,106 (1963), 210–221. · Zbl 0123.03601 · doi:10.1090/S0002-9947-1963-0144926-7
[16] —-, Asymptotic Factorization of Ideals,J. London Math. Soc.,38 (1963), 341–350. · Zbl 0142.28802 · doi:10.1112/jlms/s1-38.1.341
[17] D. Mumford, The topology of normal singularities of an algebraic surface,Publ. Math. Inst. Hautes Études Sci., no 9, 1961. · Zbl 0108.16801
[18] –, Lectures on Curves on an Algebraic Surface,Ann. of Math. Studies, no 59, Princeton, 1966. · Zbl 0187.42701
[19] M. Nagata,Local Rings, Interscience, New York, 1962.
[20] F. Oort,Reducible and Multiple Algebraic Curves, Assen, Van Gorcum, 1961. · Zbl 0102.15905
[21] G. Scheja, Einige Beispiele faktorieller lokaler Ringe,Math. Annalen,172 (1967), 124–134. · Zbl 0147.01602 · doi:10.1007/BF01350093
[22] I. R. Shafarevich, Lectures on Minimal Models and Birational Transformations of Two-dimensional Schemes, Tata Institute of Fundamental Research,Lectures on Mathematics, no 37, Bombay, 1966. · Zbl 0164.51704
[23] O. Zariski, Polynomial ideals defined by infinitely near base points,Ann. J. Math.,60 (1937), 151–204. · Zbl 0018.20101
[24] —-, The reduction of the singularities of an algebraic surface,Ann. of Math.,40 (1939), 639–689. · JFM 65.1399.03 · doi:10.2307/1968949
[25] —-, The reduction of the singularities of an algebraic variety,Trans. Amer. Math. Soc.,62 (1947), 1–52. · Zbl 0031.26101 · doi:10.1090/S0002-9947-1947-0021694-1
[26] –, Introduction to the Problem of Minimal Models in the Theory of Algebraic Surfaces,Publ. Math. Societ. of Japan, no 4, Tokyo, 1958. · Zbl 0093.33904
[27] —-, andP. Samuel,Commutative Algebra, vol. 2, Princeton, Van Nostrand, 1960.
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