About counterexamples for generalized Zariski cancellation problem

Abstract

We investigate principal -bundles over pre-varieties which play an important role for the moduli of counter examples for Generalized Zariski Cancelation Problem. In this paper we give three important theorem for this problem; a criterion for a principal -bundle over a pre-variety of a certain type to be affine, a criterion for two principal -bundles to be isomorphic, and the uniqueness of the base schemes of principal -bundle structures in the case that there exists a base scheme having a dominant morphism to a variety of nonnegative logarithmic Kodaira dimension.