×

Some open questions in the theory of singularities. (English) Zbl 0236.14002


MSC:

14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
14B05 Singularities in algebraic geometry
32Sxx Complex singularities
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Shreeram Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic \?\ne 0, Ann. of Math. (2) 63 (1956), 491 – 526. · Zbl 0108.16803 · doi:10.2307/1970014
[2] Shreeram S. Abhyankar, Resolution of singularities of arithmetical surfaces, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 111 – 152.
[3] Shreeram Shankar Abhyankar, Resolution of singularities of embedded algebraic surfaces, Pure and Applied Mathematics, Vol. 24, Academic Press, New York-London, 1966. · Zbl 0147.20504
[4] Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109 – 203; ibid. (2) 79 (1964), 205 – 326. · Zbl 0122.38603
[5] Heisuke Hironaka, Normal cones in analytic Whitney stratifications, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 127 – 138. · Zbl 0219.57022
[6] John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. · Zbl 0184.48405
[7] R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969), 240 – 284 (French). · Zbl 0197.20502
[8] Hassler 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. · Zbl 0006.37101
[9] Hassler Whitney, Tangents to an analytic variety, Ann. of Math. (2) 81 (1965), 496 – 549. · Zbl 0152.27701 · doi:10.2307/1970400
[10] Oscar Zariski, The reduction of the singularities of an algebraic surface, Ann. of Math. (2) 40 (1939), 639 – 689. · Zbl 0021.25303 · doi:10.2307/1968949
[11] Oscar Zariski, Local uniformization on algebraic varieties, Ann. of Math. (2) 41 (1940), 852 – 896. · Zbl 0025.21601 · doi:10.2307/1968864
[12] Oscar Zariski, A simplified proof for the resolution of singularities of an algebraic surface, Ann. of Math. (2) 43 (1942), 583 – 593. · Zbl 0063.08389 · doi:10.2307/1968814
[13] Oscar Zariski, Reduction of the singularities of algebraic three dimensional varieties, Ann. of Math. (2) 45 (1944), 472 – 542. · Zbl 0063.08361 · doi:10.2307/1969189
[14] Oscar Zariski, Studies in equisingularity. I. Equivalent singularities of plane algebroid curves, Amer. J. Math. 87 (1965), 507 – 536. · Zbl 0132.41601 · doi:10.2307/2373019
[15] Oscar Zariski, Studies in equisingularity. II. Equisingularity in codimension 1 (and characteristic zero), Amer. J. Math. 87 (1965), 972 – 1006. · Zbl 0146.42502 · doi:10.2307/2373257
[16] Oscar Zariski, Studies in equisingularity. III. Saturation of local rings and equisingularity, Amer. J. Math. 90 (1968), 961 – 1023. · Zbl 0189.21405 · doi:10.2307/2373492
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.