Classification of open algebraic surfaces and its applications

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I gave a structure theorem for the open algebraic surfaces of logarithmic Kodaira dimension one in arbitrary characteristic and, by using the structure theorem, I gave a relation of logarithmic Kodaira dimension and logarithmic plurigenera for an irrational algebraic surface. Moreover, I had studied kernels of higher derivations in polynomial rings and clarified the structure of the kernels of higher derivations in polynomial rings in two variables over an integral domain. By using the results obtained in this research, I classified some normal del Pezzo surfaces of Picard number one with only log canonical singular points and clarified the structure of the normal affine surfaces with non-positive Euler numbers.