# On Smooth Divisors of a Projective Hypersurface

Research paper by Ph. Ellia, D. Franco

Indexed on: 24 Jun '04Published on: 24 Jun '04Published in: Mathematics - Algebraic Geometry

#### Abstract

We prove an effective bound for the degree of a smooth divisor of a hypersurface of P^n, 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.