About counterexamples for generalized Zariski cancellation problem

Abstract

We investigate principal ${\mathbb{G}}_a$-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 ${\mathbb{G}}_a$-bundle over a pre-variety of a certain type to be affine, a criterion for two principal ${\mathbb{G}}_a$-bundles to be isomorphic, and the uniqueness of the base schemes of principal ${\mathbb{G}}_a$-bundle structures in the case that there exists a base scheme having a dominant morphism to a variety of nonnegative logarithmic Kodaira dimension.

Keywords:

• Zariski cancellation problem
• principal G_a bundle

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 14R10