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Some open questions in the theory of singularities
Author:
Oscar Zariski
Journal:
Bull. Amer. Math. Soc. 77 (1971), 481-491
MSC (1970):
Primary 14B05, 32C40; Secondary 14H20, 32C45
MathSciNet review:
0277533
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
Shreeram
Abhyankar, Local uniformization on algebraic surfaces over ground
fields of characteristic 𝑝≠0, Ann. of Math. (2)
63 (1956), 491–526. MR 0078017
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- 2.
Shreeram
S. Abhyankar, Resolution of singularities of arithmetical
surfaces, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ.,
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Shankar Abhyankar, Resolution of singularities of embedded
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- 4.
Heisuke
Hironaka, Resolution of singularities of an algebraic variety over
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0239612 (39 #969)
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Whitney, Local properties of analytic varieties, Differential
and Combinatorial Topology (A Symposium in Honor of Marston Morse),
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- 9.
Hassler
Whitney, Tangents to an analytic variety, Ann. of Math. (2)
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(33 #745)
- 10.
Oscar
Zariski, The reduction of the singularities of an algebraic
surface, Ann. of Math. (2) 40 (1939), 639–689.
MR
0000159 (1,26d)
- 11.
Oscar
Zariski, Local uniformization on algebraic varieties, Ann. of
Math. (2) 41 (1940), 852–896. MR 0002864
(2,124a)
- 12.
Oscar
Zariski, A simplified proof for the resolution of singularities of
an algebraic surface, Ann. of Math. (2) 43 (1942),
583–593. MR 0006851
(4,52c)
- 13.
Oscar
Zariski, Reduction of the singularities of algebraic three
dimensional varieties, Ann. of Math. (2) 45 (1944),
472–542. MR 0011006
(6,102f)
- 14.
Oscar
Zariski, Studies in equisingularity. I. Equivalent singularities of
plane algebroid curves, Amer. J. Math. 87 (1965),
507–536. MR 0177985
(31 #2243)
- 15.
Oscar
Zariski, Studies in equisingularity. II. Equisingularity in
codimension 1 (and characteristic zero), Amer. J. Math.
87 (1965), 972–1006. MR 0191898
(33 #125)
- 16.
Oscar
Zariski, Studies in equisingularity. III. Saturation of local rings
and equisingularity, Amer. J. Math. 90 (1968),
961–1023. MR 0237493
(38 #5775)
- 1.
- S. Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic $p\ne 0$, Ann. of Math. (2) 63 (1956), 491-526; Correction, ibid. (2) 78 (1963), 202-203. MR 17, 1134; MR 27 #145. MR 78017
- 2.
- S. Abhyankar, Resolution of singularities of arithmetical surfaces, Proc. Conf. Arithmetical Algebraic Geometry (Purdue University, 1963), Harper & Row, New York, 1965, pp. 111-152. MR 34 #171. MR 200272
- 3.
- S. Abhyankar, Resolution of singularities of embedded algebraic surfaces. Pure and Appl. Math., vol. 24, Academic Press, New York, 1966. MR 36 #164. MR 217069
- 4.
- H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109-326. MR 33 #7333. MR 199184
- 5.
- H. Hironaka, Normal cones in analytic Whitney stratifications, Inst. HAutes Études Sci. Publ. Math. No. 36 (1969), 127-138. MR 277759
- 6.
- J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Studies, no. 61, Princeton Univ. Press, Princeton, N. J.; Univ. of Tokyo Press, Tokyo, 1968. MR 39 #969. MR 239612
- 7.
- R. Thorn, Ensembles et morphismes stratifies, Bull. Amer. Math. Soc. 75 (1969), 240-284. MR 39 #970. MR 239613
- 8.
- H. Whitney, Local properties of analytic varieties, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N. J., 1965, pp. 205-244. MR 32 #5924. MR 188486
- 9.
- H. Whitney, Tangents to an analytic variety, Ann. of Math. (2) 81 (1965), 496-549. MR 33 #745. MR 192520
- 10.
- O. Zariski, The reduction of the singularities of an algebraic surface, Ann. of Math. (2) 40 (1939), 639-689. MR 1, 26. MR 159
- 11.
- O. Zariski, Local uniformization on algebraic varieties, Ann. of Math. (2) 41 (1940), 852-896. MR 2, 124. MR 2864
- 12.
- O. Zariski, Simplified proof for the resolution of singularities of an algebraic surface, Ann. of Math. (2) 43 (1942), 583-593. MR4, 52. MR 6851
- 13.
- O. Zariski, Reduction of the singularities of algebraic three dimensional varieties, Ann. of Math. (2) 45 (1944), 472-542. MR 6, 102. MR 11006
- 14.
- O. Zariski, Studies in equisingularity. I. Equivalent singularities of plane algebroid curves, Amer. J. Math. 87 (1965), 507-536. MR 31 #2243. MR 177985
- 15.
- O. Zariski, Studies in equisingularity. II. Equisingularity in codimension 1 (and characteristic zero), Amer. J. Math. 87 (1965), 972-1006. MR 33 #125. MR 191898
- 16.
- O. Zariski, Studies in equisingularity. III. Saturation of local rings and equisingularity, Amer. J. Math. 90 (1968), 961-1023. MR 38 #5775. MR 237493
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1971-12729-5
PII:
S 0002-9904(1971)12729-5
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