2011/12/31 by Karl Schwede, Wenliang Zhang · 1 citation
Mathematics · #math.AG #math.AC #msc:14F18 #msc:13A35 #msc:14E15 #msc:14J17 #msc:14B05
paper · pdf · doi:10.1112/plms/pdt007
published as Proc. London Math. Soc. (2013) 107 (4): 851-874 · Typos corrected and other minor changes. To appear in the Proceedings of the London Mathematical Society
arxiv created 2013/01/03 · arxiv updated 2014/02/26
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.