Abstract
The purpose of this paper is to explain a method on the generalization of the Bertini-type theorem on standard graded rings to the non-standard graded case of certain type.
Acknowledgments
The author is grateful to Professor L. Katthän and Professor K. Yanagawa for sharing illuminating discussions. The author is grateful to the referee for some kind comments.
Notes
1 Here, the module-finite condition ensures that is indeed a morphism. In general, the map of graded rings does not necessarily induce a map on the corresponding projective schemes; rather it is defined over some subset.