Rational singularities with applications to algebraic surfaces and unique factorization
Publications Mathématiques de l'IHÉS, Tome 36 (1969), pp. 195-279 
@article{PMIHES_1969__36__195_0,
     author = {Lipman, Joseph},
     title = {Rational singularities with applications to algebraic surfaces and unique factorization},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {195--279},
     year = {1969},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {36},
     mrnumber = {276239},
     zbl = {0181.48903},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1969__36__195_0/}
}
TY  - JOUR
AU  - Lipman, Joseph
TI  - Rational singularities with applications to algebraic surfaces and unique factorization
JO  - Publications Mathématiques de l'IHÉS
PY  - 1969
SP  - 195
EP  - 279
VL  - 36
PB  - Institut des Hautes Etudes Scientifiques
UR  - https://www.numdam.org/item/PMIHES_1969__36__195_0/
LA  - en
ID  - PMIHES_1969__36__195_0
ER  - 
%0 Journal Article
%A Lipman, Joseph
%T Rational singularities with applications to algebraic surfaces and unique factorization
%J Publications Mathématiques de l'IHÉS
%D 1969
%P 195-279
%V 36
%I Institut des Hautes Etudes Scientifiques
%U https://www.numdam.org/item/PMIHES_1969__36__195_0/
%G en
%F PMIHES_1969__36__195_0
Lipman, Joseph. Rational singularities with applications to algebraic surfaces and unique factorization. Publications Mathématiques de l'IHÉS, Tome 36 (1969), pp. 195-279. https://www.numdam.org/item/PMIHES_1969__36__195_0/

[1] S. S. Abhyankar, On the valuations centered in a local domain, Amer. J. Math., 78 (1956), 321-348. | Zbl | MR

[2] S. S. Abhyankar, Resolution of singularities of arithmetical surfaces, pp. 111-152, in Arithmetical Algebraic Geometry, New York, Harper and Row, 1965 (edited by O. F. G. SCHILLING). | Zbl | MR

[3] M. Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math., 84 (1962), 485-496. | Zbl | MR

[4] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math., 88 (1966), 129-136. | Zbl | MR

[5] N. Bourbaki, Algèbre commutative, chap. 5-6, Act. Sci. et Ind., n° 1308, Paris, Hermann, 1964. | Zbl

[6] E. Brieskorn, Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen, Math. Annalen, 166 (1966), 76-102. | Zbl | MR

[7] E. Brieskorn, Rationale Singularitäten komplexer Flächen, Inventiones Math., 4 (1968), 336-358. | Zbl | MR

[7 1/2] 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. | Zbl | JFM

[8] (cited [EGA...]), A. Grothendieck and J. Dieudonné, Éléments de Géométrie algébrique, Publ. Math. Inst. Hautes Études Sci., n°s 4, 8, ..., 32 (1960, ..., 1967). | Numdam

[9] H. Hironaka, Desingularization of excellent surfaces, Advanced Science Seminar in Algebraic Geometry, Bowdoin College, Brunswick, Maine, 1967.

[10] H. Hironaka, Forthcoming paper on desingularization of excellent surfaces, J. Math. Kyoto Univ.

[11] S. Kleiman, Toward a numerical theory of ampleness, Ann. of Math., 84 (1966), 293-344. | Zbl | MR

[12] W. Krull, Beiträge zur Arithmetik kommutativer Integritätsbereiche, Math. Z., 41 (1936), 545-577. | JFM

[13] S. Lichtenbaum, Curves over discrete valuation rings, Amer. J. Math., 90 (1968), 380-405. | Zbl | MR

[14] H. T. Muhly and M. Sakuma, Some multiplicative properties of complete ideals, Trans. Amer. Math. Soc., 106 (1963), 210-221. | Zbl | MR

[14'] H. T. Muhly and M. Sakuma, Asymptotic Factorization of Ideals, J. London Math. Soc., 38 (1963), 341-350. | Zbl | MR

[15] D. Mumford, The topology of normal singularities of an algebraic surface, Publ. Math. Inst. Hautes Études Sci., n° 9, 1961. | Zbl | MR | Numdam

[16] D. Mumford, Lectures on Curves on an Algebraic Surface, Ann. of Math. Studies, n° 59, Princeton, 1966. | Zbl | MR

[17] M. Nagata, Local Rings, Interscience, New York, 1962. | Zbl | MR

[18] F. Oort, Reducible and Multiple Algebraic Curves, Assen, Van Gorcum, 1961. | Zbl | MR

[19] G. Scheja, Einige Beispiele faktorieller lokaler Ringe, Math. Annalen, 172 (1967), 124-134. | Zbl | MR

[20] I. R. Shafarevich, Lectures on Minimal Models and Birational Transformations of Two-dimensional Schemes, Tata Institute of Fundamental Research, Lectures on Mathematics, n° 37, Bombay, 1966. | Zbl | MR

[21] O. Zariski, Polynomial ideals defined by infinitely near base points, Amer. J. Math., 60 (1937), 151-204. | Zbl | JFM

[22] O. Zariski, The reduction of the singularities of an algebraic surface, Ann. of Math., 40 (1939), 639-689. | Zbl | MR | JFM

[23] O. Zariski, The concept of a simple point of an abstract algebraic variety, Trans. Amer. Math. Soc., 62 (1947), 1-52. | Zbl | MR

[24] O. Zariski, Introduction to the Problem of Minimal Models in the Theory of Algebraic Surfaces, Publ. Math. Societ. of Japan, n° 4, Tokyo, 1958. | Zbl | MR

[25] O. Zariski and P. Samuel, Commutative Algebra, vol. 2, Princeton, Van Nostrand, 1960. | Zbl | MR