Strong Bertini theorems
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- by Steven Diaz and David Harbater PDF
- Trans. Amer. Math. Soc. 324 (1991), 73-86 Request permission
Abstract:
We show that the singular locus of the general member of a linear system has dimension less than that predicted by Bertini’s theorem, provided that the base locus is scheme-theoretically smooth. As corollaries, we obtain a result about complete intersection varieties containing a given subvariety and a result concerning liaison.References
- William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620, DOI 10.1007/978-3-662-02421-8
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157 —, Ample subvarieties of projective varieties, Lecture Notes in Math., vol. 156, Springer-Verlag, Heidelberg, 1970.
- Robin Hartshorne, Complete intersections and connectedness, Amer. J. Math. 84 (1962), 497–508. MR 142547, DOI 10.2307/2372986
- Robin Hartshorne, Varieties of small codimension in projective space, Bull. Amer. Math. Soc. 80 (1974), 1017–1032. MR 384816, DOI 10.1090/S0002-9904-1974-13612-8
- Craig Huneke and Bernd Ulrich, The structure of linkage, Ann. of Math. (2) 126 (1987), no. 2, 277–334. MR 908149, DOI 10.2307/1971402 Mieo Nishi, On the imbedding of a nonsingular variety in an irreducible complete intersection, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 29 (1955), 172-187.
- Oscar Zariski, The theorem of Bertini on the variable singular points of a linear system of varieties, Trans. Amer. Math. Soc. 56 (1944), 130–140. MR 11572, DOI 10.1090/S0002-9947-1944-0011572-3
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 324 (1991), 73-86
- MSC: Primary 14C20
- DOI: https://doi.org/10.1090/S0002-9947-1991-0986689-6
- MathSciNet review: 986689