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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Strong Bertini theorems


Authors: Steven Diaz and David Harbater
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1991-0986689-6
Keywords: Bertini theorem, complete intersection, liaison
Article copyright: © Copyright 1991 American Mathematical Society