Analysis of structures on affine algebraic varieties from the viewpoint of log minimal model theory

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In the present project of research, I devoted mainly myself to the analysis of structures on affine algebraic varieties from the various points of view. More precisely, in the first viewpoint, I succeeded into the translation of the existence of actions of a 1-dimensional additive group on affine cones over polarized projective varieties into the existence of certain kinds of open subset contained in the polarized varieties. In the second, I could reduce the homogeneous action of a 1-dimensional additive group on the affine 3-space to linear pencil of rational curves with special properties on weighted projective planes to be able to produce plenty of complicated automorphisms.