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  • 1.
    Källström, Rolf
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Preservation of defect sub-schemes by the action of the tangent sheaf2005In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 203, no 1-3, p. 166-188Article in journal (Refereed)
    Abstract [en]

    Let X/S be a noetherian scheme with a coherent -module M, and TX/S be the relative tangent sheaf acting on M. We give constructive proofs that sub-schemes Y, with defining ideal IY, of points xX where or Mx is “bad”, are preserved by TX/S, making certain assumptions on X/S. Here bad means one of the following: is not normal; has high regularity defect; does not satisfy Serre's condition (Rn); has high complete intersection defect; is not Gorenstein; does not satisfy (Tn); does not satisfy (Gn); is not n-Gorenstein; Mx is not free; Mx has high Cohen–Macaulay defect; Mx does not satisfy Serre's condition (Sn); Mx has high type. Kodaira–Spencer kernels for syzygies are described, and we give a general form of the assertion that M is locally free in certain cases if it can be acted upon by TX/S.

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