On Smooth Divisors of a Projective Hypersurface

2004/06/24 by Ph. Ellia, D. Franco, Ellia, Ph. +1
Mathematics · #14M06 #14M10 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14M06 #msc:14M10 #msc:14N05

paper · pdf · doi:10.48550/arxiv.math/0406497

arxiv created 2004/06/24 · arxiv updated 2009/12/01

Abstract

We prove an effective bound for the degree of a smooth divisor of a hypersurface of Pⁿ, n>4 (projective space over an algebraically closed field of characteristic zero). Our result follows from a strong (since the degree of the divisor is not involved) generalization of the "Speciality theorem" of Gruson-Peskine, which we prove to hold for any smooth, subcanonical, codimension two, projective verieties of dimension at least three.

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