Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multisecant subspaces to smooth projective varieties in arbitrary characteristic


Author: Atsushi Noma
Journal: Proc. Amer. Math. Soc. 137 (2009), 3985-3990
MSC (2000): Primary 14N05, 14H45
Published electronically: July 1, 2009
MathSciNet review: 2538558
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X \subseteq \mathbb{P}^{N}$ be a projective variety of dimension $ n\geq 1$, degree $ d$, and codimension $ e$, not contained in any hyperplane, defined over an algebraically closed field $ \Bbbk$ of arbitrary characteristic. We show that if a $ k$-dimensional linear subspace $ M$ meets $ X$ at the smooth locus such that $ X\cap M$ is finite and locally lies on a smooth curve, then the length $ l(X\cap M)$ does not exceed $ d-e+k-\min \{g,e-k\}$ for the sectional genus $ g$ of $ X$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14N05, 14H45

Retrieve articles in all journals with MSC (2000): 14N05, 14H45


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09977-8
PII: S 0002-9939(09)09977-8
Keywords: Secant line, secant space, sectional genus
Received by editor(s): June 1, 2007
Received by editor(s) in revised form: March 20, 2009
Published electronically: July 1, 2009
Additional Notes: This work was partially supported by the Japan Society for the Promotion of Science.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.