Strong bertini theorems

Steven Diaz; David Harbater

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

Strong bertini theorems

Steven Diaz, David Harbater

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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.

Original language	English (US)
Pages (from-to)	73-86
Number of pages	14
Journal	Transactions of the American Mathematical Society
Volume	324
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1991-0986689-6
State	Published - Mar 1991

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1991-0986689-6

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title = "Strong bertini theorems",

abstract = "We show that the singular locus of the general member of a linear system has dimension less than that predicted by Bertini{\textquoteright}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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AB - 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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Strong bertini theorems

Abstract

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