Projective varieties with nonbirational linear projections and applications

摘要

We work over an algebraically closed field of characteristic zero. The purpose of this paper is to characterize a nondegenerate projective variety $ X$ with a linear projection which induces a nonbirational map to its image. As an application, for smooth $ X$ of degree $ d$ and codimension $ e$, we prove the ``semiampleness'' of the $ (d-e+1)$th twist of the ideal sheaf. This improves a linear bound of the regularity of smooth projective varieties by Bayer-Mumford-Bertram-Ein-Lazarsfeld, and gives an asymptotic regularity bound.