Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic

Abstract: This paper aims to investigate effectivity problems of pluricanonical systems on varieties of general type in positive characteristic. In practice, we will consider a sub-linear system $|S^0_{-}(X, K_X + nK_X)| \subseteq |H^0(X, K_X +nK_X)|$ generated by certain Frobenius stable sections, and prove that for a minimal terminal threefold $X$ of general type with either $q(X)>0$ or Gorenstein singularities, if $n\geq 28$ then $|S^0_{-}(X, K_X + nK_X)| \neq \emptyset$; if $n\geq 42$ then the linear system $|S^0_{-}(X, K_X + nK_X)|$ defines a birational map.