On a conormal module of smooth set theoretic complete intersections

Boratyński, M.

doi:10.1090/S0002-9947-1986-0837812-3

On a conormal module of smooth set theoretic complete intersections
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by M. Boratyński

Trans. Amer. Math. Soc. 296 (1986), 291-300

DOI: https://doi.org/10.1090/S0002-9947-1986-0837812-3

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Abstract:

We prove that $V \subset {\mathbf {A}}_k^n$ ($V$-smooth) is a set-theoretic complete intersection (stci) if and only if $V$ imbedded as a zero section of its normal bundle is a stci, we give a characterization of smooth codimension $2$ stci of index $\leq 4$ in terms of their conormal modules.

References

Hyman Bass, Projective modules and symmetric algebras, Monografías de Matemática [Mathematical Monographs], vol. 30, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1978. MR 527279
M. Boratyński, A note on set-theoretic complete intersection ideals, J. Algebra 54 (1978), no. 1, 1–5. MR 511453, DOI 10.1016/0021-8693(78)90017-0
Maksymillian Boratyński, Poincaré forms, Gorenstein algebras and set theoretic complete intersections, Complete intersections (Acireale, 1983) Lecture Notes in Math., vol. 1092, Springer, Berlin, 1984, pp. 270–290. MR 775889, DOI 10.1007/BFb0099369
David Eisenbud and E. Graham Evans Jr., Generating modules efficiently: theorems from algebraic $K$-theory, J. Algebra 27 (1973), 278–305. MR 327742, DOI 10.1016/0021-8693(73)90106-3
Manfred Knebusch, Symmetric bilinear forms over algebraic varieties, Conference on Quadratic Forms—1976 (Proc. Conf., Queen’s Univ., Kingston, Ont., 1976) Queen’s Papers in Pure and Appl. Math., No. 46, Queen’s Univ., Kingston, Ont., 1977, pp. 103–283. MR 0498378
Hartmut Lindel, On projective modules over polynomial rings over regular rings, Algebraic $K$-theory, Part I (Oberwolfach, 1980) Lecture Notes in Math., vol. 966, Springer, Berlin-New York, 1982, pp. 169–179. MR 689374
Günter Scheja and Uwe Storch, Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte, Manuscripta Math. 19 (1976), no. 1, 75–104. MR 407039, DOI 10.1007/BF01172339