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.