We classify purely inseparable morphisms of degree $p$ between rational double points (RDPs) in characteristic $p$. Using such morphisms, we show that any RDP admit a finite smooth covering.

We prove that no regular vector field exists on an algebraic K3 surface defined over an algebraically closed field of finite characteristic.Bibliography: 19 titles.

We give lower bounds of, or moreover determine, the height of K3 surfaces in characteristic $p$ admitting non-taut rational double point singularities or actions of local group schemes of order $p$… Expand