×
Roberts, Joel

Singularity subschemes and generic projections. (English) Zbl 0314.14003

Trans. Am. Math. Soc. 212, 229-268 (1975).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0314.14003

Cited in 2 Reviews
Cited in 12 Documents

MSC:

14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14N05 Projective techniques in algebraic geometry
14B05 Singularities in algebraic geometry
Cite Review PDF
Full Text: DOI

References:

[1] J. M. Boardman, Singularities of differentiable maps, Inst. Hautes Études Sci. Publ. Math. 33 (1967), 21 – 57. · Zbl 0165.56803
[2] J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them., Proc. Roy. Soc. Ser. A 269 (1962), 188 – 204. · Zbl 0106.25603
[3] H. Fitting, Die Determinantenideale eines Moduls, Jber. Deutsch. Math.-Verein. 46 (1936), 195-228. · Zbl 0016.05003
[4] A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas, 4e partie,Rédigés avec la collaboration de J. Dieudonné, Inst. Hautes Études Sci. Publ. Math. No. 32 (1967). MR 39 #220. · Zbl 0153.22301
[5] Harold I. Levine, The singularities, \?\(_{1}\)^{\?}, Illinois J. Math. 8 (1964), 152 – 168. · Zbl 0124.38801
[6] John N. Mather, Generic projections, Ann. of Math. (2) 98 (1973), 226 – 245. · Zbl 0242.58001 · doi:10.2307/1970783
[7] Bernard Morin, Formes canoniques des singularités d’une application différentiable, C. R. Acad. Sci. Paris 260 (1965), 5662 – 5665 (French). · Zbl 0178.26801
[8] K. R. Mount and O. E. Villamayor, An algebraic construction of the generic singularities of Boardman-Thom, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 205 – 244. · Zbl 0283.57013
[9] Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. · Zbl 0123.03402
[10] D. G. Northcott, Some remarks on the theory of ideals defined by matrices, Quart. J. Math. Oxford Ser. (2) 14 (1963), 193 – 204. · Zbl 0116.02504 · doi:10.1093/qmath/14.1.193
[11] Joel Roberts, Generic projections of algebraic varieties, Amer. J. Math. 93 (1971), 191 – 214. · Zbl 0212.53801 · doi:10.2307/2373457
[12] Joel Roberts, The variation of singular cycles in an algebraic family of morphisms, Trans. Amer. Math. Soc. 168 (1972), 153 – 164. · Zbl 0241.14005
[13] Joel Roberts, Singularity subschemes and generic projections, Bull. Amer. Math. Soc. 78 (1972), 706 – 708. · Zbl 0255.14005
[14] -, Generic coverings of \( {P^r}\) when \( {\text{char}}(k) > 0\), Notices Amer. Math. Soc. 20 (1973), A-383. Abstract #704-A5.
[15] Satoshi Suzuki, Differentials of commutative rings, Queen’s University, Kingston, Ont., 1971. Queen’s Papers in Pure and Applied Mathematics, No. 29. · Zbl 0271.12104
[16] R. Thom, Les singularités des applications différentiables, Ann. Inst. Fourier, Grenoble 6 (1955 – 1956), 43 – 87 (French). · Zbl 0075.32104
[17] Hassler Whitney, Singularities of mappings of Euclidean spaces, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 285 – 301. · Zbl 0092.28401
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.