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

DOI:
https://doi.org/10.1090/S0002-9939-09-09977-8

Published electronically:
July 1, 2009

MathSciNet review:
2538558

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a projective variety of dimension , degree , and codimension , not contained in any hyperplane, defined over an algebraically closed field of arbitrary characteristic. We show that if a -dimensional linear subspace meets at the smooth locus such that is finite and locally lies on a smooth curve, then the length does not exceed for the sectional genus of .

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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:
https://doi.org/10.1090/S0002-9939-09-09977-8

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.