Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Laudal's lemma in positive characteristic

Author: Paola Bonacini
Journal: J. Algebraic Geom. 18 (2009), 459-475
Published electronically: July 3, 2008
MathSciNet review: 2496454
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Abstract: Laudal's lemma states that if $ C$ is a curve of degree $ d>s^2+1$ in $ \mathbb{P}^3$ over an algebraically closed field of characteristic 0 such that its plane section is contained in an irreducible curve of degree $ s$, then $ C$ lies on a surface of degree $ s$. We show that the same result does not hold in positive characteristic and we find different bounds $ d>f(s)$ which ensure that $ C$ is contained in a surface of degree $ s$.

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Paola Bonacini
Affiliation: University of Catania, Viale A. Doria 6, 95124, Catania, Italy

Received by editor(s): January 26, 2007
Received by editor(s) in revised form: September 30, 2007
Published electronically: July 3, 2008