Pacific Journal of Mathematics

Determinantal criteria for transversality of morphisms.

Dan Laksov and Robert Speiser

Article information

Source
Pacific J. Math., Volume 156, Number 2 (1992), 307-328.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102634980

Mathematical Reviews number (MathSciNet)
MR1186808

Zentralblatt MATH identifier
0789.14010

Subjects
Primary: 14M12: Determinantal varieties [See also 13C40]
Secondary: 14A15: Schemes and morphisms

Citation

Laksov, Dan; Speiser, Robert. Determinantal criteria for transversality of morphisms. Pacific J. Math. 156 (1992), no. 2, 307--328. https://projecteuclid.org/euclid.pjm/1102634980


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References

  • [6] Applications tovarieties. Here we show howthe transversality criteria ofKleiman and Laksov, described inthe introduction, follow directly from the results ofthe last twosections. Throughout this section, weshall assume that thebase scheme S is the spectrum ofanalgebraically closed field k. Then, byHubert's Nullstellensatz, the /c-points of any S-scheme form a dense subset. We shall need the following result, which holds over any smooth base scheme.
  • [1] A. Altman andS. L. Kleiman, Introduction to Grothendieck Duality Theory, Lecture Notes inMath.,vol. 146, Springer-Verlag, New York-Heidelberg-Berlin, 1970.
  • [2] A.Grothendieck (with J.Dieudonne),Elements degomtrie algbrique, Chap. IV, Publ. Math, deI.H.E.S.,20 (1964), 24 (1964), 28 (1966), 32 (1967).
  • [3] R. Hartshorne,Algebraic Geometry, Springer GTM 52,New York-Heidelberg- Berlin, (1977).
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  • [6] D.Laksov andR. Speiser, Transversality Criteria in any Characteristic, Proc. 1987 Sitges conference onenumerative geometry, Lecture Notes in Math., vol. 1436, Springer-Verlag, New York-Heidelberg-Berlin, 1990, pp. 139-150.
  • [7] R.Speiser, TransversalityTheorems for Families of Maps, Proc. 1986 Sundance Conference, Lecture Notes in Math., vol. 1311,Springer-Verlag, NewYork- Heidelberg-Berlin, 1988, pp. 235-252.
  • [8] O. Zariski, Thetheorem of Bertini on the variable singular points of a linear system of varieties, Trans. Amer. Math. Soc, 56(1944), 130-140; also Collected papers, v.l, MIT Press, (1972), 242-252.