Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Projective varieties with nonbirational linear projections and applications

Author: Atsushi Noma
Journal: Trans. Amer. Math. Soc. 370 (2018), 2299-2320
MSC (2010): Primary 14N05, 14N15
Published electronically: December 18, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14N05, 14N15

Retrieve articles in all journals with MSC (2010): 14N05, 14N15

Additional Information

Atsushi Noma
Affiliation: Faculty of Engineering Sciences, Department of Mathematics, Yokohama National University, Yokohama 240-8501 Japan
Email: noma@\

Keywords: Linear projection, Castelnuovo--Mumford regularity, ideal sheaf
Received by editor(s): July 1, 2014
Received by editor(s) in revised form: April 28, 2016
Published electronically: December 18, 2017
Additional Notes: This paper was partially supported by Grant-in-Aid for Scientific Research (C), 20540039, 23540043, and 26400041 Japan Society for the Promotion of Science.
Article copyright: © Copyright 2017 American Mathematical Society