We show that the Bogomolov-Sommese vanishing theorem holds for a log canonical projective surface (X,B) in large characteristic unless Iitaka dimension of KX+?B? is not equal to two. As an application, we prove resolution pair normal and reduced divisor lifts ring Witt vectors when less than or zero. Moreover, give explicit optimal bounds on their dimensions are

Abstract The ship hull form is directly related to each design phase of a ship. This thus frequently designed based on variation well-made parent avoid new risks. However, in variation, satisfactory geometric preservation and good performance continuity the are considered competing requirements. To effectively facilitate an appropriate compromise between these requirements should be achieved. I...