Defining ideals of projective varieities and their embedding structure

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For a projective variety, a point from which the variety is projected nonbirationaly onto its image is called a nonbirational center. In this research, we obtained a characterization of projective varieties with nonbirational center(s). As applications of this characterization, for a smooth projective variety, we showed some semiampleness of its ideal sheaf and improved the regularity bound of the ideal sheaf. On the other hand, as an application of linear projections, we show the very ampleness of the double-point divisor of a projective variety.