Generic inner projections of projective varieties and an application to the positivity of double point divisors
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Abstract:
Let $X\subseteq \mathbb {P}^{N}$ be a smooth nondegenerate projective variety of dimension $n\geq 2$, codimension $e$ and degree $d$ with the canonical line bundle $\omega _{X}$ defined over an algebraically closed field of characteristic zero. The purpose here is to prove that the base locus of $|\mathcal {O}_{X}(d-n-e-1)\otimes \omega _{X}^{\vee }|$ is at most a finite set, except in a few cases. To describe the exceptional cases, we classify (not necessarily smooth) projective varieties whose generic inner projections have exceptional divisors. As applications, we prove the $(d-e)$-regularity of $\mathcal {O}_{X}$, Property $(N_{k-d+e})$ for $\mathcal {O}_{X}(k)$, and inequalities for the delta and sectional genera.References
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Additional Information
- Atsushi Noma
- Affiliation: Department of Mathematics, Yokohama National University, Yokohama 240-8501 Japan
- MR Author ID: 315999
- Email: noma@ynu.ac.jp
- Received by editor(s): September 28, 2011
- Received by editor(s) in revised form: August 23, 2012
- Published electronically: May 12, 2014
- Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 4603-4623
- MSC (2010): Primary 14N15, 14N05
- DOI: https://doi.org/10.1090/S0002-9947-2014-06129-1
- MathSciNet review: 3217694