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
DOI: https://doi.org/10.1090/S1056-3911-08-00501-8
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
Email: bonacini@dmi.unict.it

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