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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
DOI: https://doi.org/10.1090/tran/7086
Published electronically: December 18, 2017
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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.


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Additional Information

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

DOI: https://doi.org/10.1090/tran/7086
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

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