Strong Bertini theorems

Diaz, Steven; Harbater, David

doi:10.1090/S0002-9947-1991-0986689-6

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.

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