Bertini theorems for F-singularities

Details Bertini theorems for F-singularities Bertini theorems for F-singularities

2011-12-09

arxiv.org/abs/1112.2161v3

Mathematics

Algebraic Geometry

Some typos corrected and a couple references added

Scientific paper

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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