Open AccessProjective varieties with nonbirational linear projections and applications
Author(s) -
Atsushi Noma
Publication year - 2017
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/7086
Subject(s) - algorithm , annotation , computer science , artificial intelligence , type (biology) , mathematics , biology , ecology
We work over an algebraically closed field of characteristic zero. The purpose of this paper is to characterize a nondegenerate projective variety X X with a linear projection which induces a nonbirational map to its image. As an application, for smooth X X of degree d d and codimension e e , we prove the “semiampleness” of the ( d − e + 1 ) (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.