On the singularities of quotients by 1-foliations

Abstract

We study the singularities of varieties obtained as infinitesimal quotients by $1$-foliations in positive characteristic. (1) We show that quotients by (log) canonical $1$-foliations preserve the (log) singularities of the MMP. (2) We prove that quotients by multiplicative derivations preserve many properties, amongst which most $F$-singularities. (3) We formulate a notion of families of $1$-foliations, and investigate the corresponding families of quotients.

v4: Final version, to appear in Nagoya Math. Journal. v5: Compared with the printed version, a few typos have been corrected and some details have been added. The main results are unchanged

References in corpus (1)

• Codimension one foliations in positive characteristic