Rational singularities with applications to algebraic surfaces and unique factorization

Joseph Lipman

Publications Mathématiques de l'IHÉS (1969)

  • Volume: 36, page 195-279
  • ISSN: 0073-8301

How to cite

top

Lipman, Joseph. "Rational singularities with applications to algebraic surfaces and unique factorization." Publications Mathématiques de l'IHÉS 36 (1969): 195-279. <http://eudml.org/doc/103893>.

@article{Lipman1969,
author = {Lipman, Joseph},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {algebraic geometry},
language = {eng},
pages = {195-279},
publisher = {Institut des Hautes Études Scientifiques},
title = {Rational singularities with applications to algebraic surfaces and unique factorization},
url = {http://eudml.org/doc/103893},
volume = {36},
year = {1969},
}

TY - JOUR
AU - Lipman, Joseph
TI - Rational singularities with applications to algebraic surfaces and unique factorization
JO - Publications Mathématiques de l'IHÉS
PY - 1969
PB - Institut des Hautes Études Scientifiques
VL - 36
SP - 195
EP - 279
LA - eng
KW - algebraic geometry
UR - http://eudml.org/doc/103893
ER -

References

top
  1. [1] S. S. ABHYANKAR, On the valuations centered in a local domain, Amer. J. Math., 78 (1956), 321-348. Zbl0074.26301MR18,556b
  2. [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). Zbl0147.20503MR34 #171
  3. [3] M. ARTIN, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math., 84 (1962), 485-496. Zbl0105.14404MR26 #3704
  4. [4] M. ARTIN, On isolated rational singularities of surfaces, Amer. J. Math., 88 (1966), 129-136. Zbl0142.18602MR33 #7340
  5. [5] N. BOURBAKI, Algèbre commutative, chap. 5-6, Act. Sci. et Ind., n° 1308, Paris, Hermann, 1964. Zbl0205.34302
  6. [6] E. BRIESKORN, Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen, Math. Annalen, 166 (1966), 76-102. Zbl0145.09402MR34 #6789
  7. [7] E. BRIESKORN, Rationale Singularitäten komplexer Flächen, Inventiones Math., 4 (1968), 336-358. Zbl0219.14003MR36 #5136
  8. [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. Zbl0010.17602JFM60.0599.01
  9. [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). 
  10. [9] H. HIRONAKA, Desingularization of excellent surfaces, Advanced Science Seminar in Algebraic Geometry, Bowdoin College, Brunswick, Maine, 1967. 
  11. [10] H. HIRONAKA, Forthcoming paper on desingularization of excellent surfaces, J. Math. Kyoto Univ. 
  12. [11] S. KLEIMAN, Toward a numerical theory of ampleness, Ann. of Math., 84 (1966), 293-344. Zbl0146.17001MR34 #5834
  13. [12] W. KRULL, Beiträge zur Arithmetik kommutativer Integritätsbereiche, Math. Z., 41 (1936), 545-577. JFM62.1105.01
  14. [13] S. LICHTENBAUM, Curves over discrete valuation rings, Amer. J. Math., 90 (1968), 380-405. Zbl0194.22101MR37 #6284
  15. [14] H. T. MUHLY and M. SAKUMA, Some multiplicative properties of complete ideals, Trans. Amer. Math. Soc., 106 (1963), 210-221. Zbl0123.03601MR26 #2466
  16. [14'] H. T. MUHLY and M. SAKUMA, Asymptotic Factorization of Ideals, J. London Math. Soc., 38 (1963), 341-350. Zbl0142.28802MR28 #3053
  17. [15] D. MUMFORD, The topology of normal singularities of an algebraic surface, Publ. Math. Inst. Hautes Études Sci., n° 9, 1961. Zbl0108.16801MR27 #3643
  18. [16] D. MUMFORD, Lectures on Curves on an Algebraic Surface, Ann. of Math. Studies, n° 59, Princeton, 1966. Zbl0187.42701MR35 #187
  19. [17] M. NAGATA, Local Rings, Interscience, New York, 1962. Zbl0123.03402MR27 #5790
  20. [18] F. OORT, Reducible and Multiple Algebraic Curves, Assen, Van Gorcum, 1961. Zbl0102.15905MR31 #4787
  21. [19] G. SCHEJA, Einige Beispiele faktorieller lokaler Ringe, Math. Annalen, 172 (1967), 124-134. Zbl0147.01602MR37 #4066
  22. [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. Zbl0164.51704MR36 #163
  23. [21] O. ZARISKI, Polynomial ideals defined by infinitely near base points, Amer. J. Math., 60 (1937), 151-204. Zbl0018.20101JFM64.0079.01
  24. [22] O. ZARISKI, The reduction of the singularities of an algebraic surface, Ann. of Math., 40 (1939), 639-689. Zbl0021.25303MR1,26dJFM65.1399.03
  25. [23] O. ZARISKI, The concept of a simple point of an abstract algebraic variety, Trans. Amer. Math. Soc., 62 (1947), 1-52. Zbl0031.26101MR9,99j
  26. [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. Zbl0093.33904MR20 #3872
  27. [25] O. ZARISKI and P. SAMUEL, Commutative Algebra, vol. 2, Princeton, Van Nostrand, 1960. Zbl0121.27801MR22 #11006

Citations in EuDML Documents

top
  1. Veronique Lierde, One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal
  2. E. Casas Alvero, Filtrations by Complete Ideals and Applications
  3. Gerardo Gonzalez-Sprinberg, Désingularisation des surfaces par des modifications de Nash normalisées
  4. Marguerite Flexor, Étude de certains éclatements
  5. M. Lejeune-Jalabert, Systèmes linéaires, idéaux complets et/ou diviseurs exceptionnels
  6. Olivier Piltant, On the Jung method in positive characteristic
  7. Joseph Lipman, Double point resolutions of deformations of rational singularities
  8. Jean Giraud, Improvement of Grauert-Riemenschneider's theorem for a normal surface
  9. Eduard Looijenga, The discriminant of a real simple singularity
  10. Michel Demazure, Classification des germes à point critique isolé et à nombres de modules 0 ou 1

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.