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

This paper investigates effectivity problems of pluricanonical systems on varieties of general type in positive characteristic. In practice, we will consider a sublinear system vertical bar S--(0)(X, K-X + nK(X))vertical bar subset of vertical bar H-0(X, K-X + nK(X))vertical bar 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 >= 28 then vertical bar S--(0)(X, K-X+nK(X))vertical bar not equal(sic); and if n >= 42 then the linear system vertical bar S--(0)(X, K-X+ nK(X))vertical bar defines a birational map.