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arXiv · 1112.2161

Bertini theorems for F-singularities

Karl Schwede·Wenliang Zhang
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Abstract

We prove that strongly F-regular and F-pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We also prove that F-injective singularities fail to satisfy even the most basic Bertini-type results.

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Karl Schwede, Wenliang Zhang. 2013-01-03. Bertini theorems for F-singularities. https://doi.org/10.1112/plms%2Fpdt007

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