On subcanonical surfaces of P^4
We prove that a smooth, subcanonical surface of P^4 (projective space over an algebraically closed field of characteristic zero) is complete intersection if it is contained in a quartic hypersurface.
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arXiv subjects
Ph. Ellia
Publications and source records attributed to Ph. Ellia.
On Smooth Divisors of a Projective Hypersurface
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.
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On smooth surfaces in P4 containing a plane curve
We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of multiplicity $(s-2)$. This implies that $S$ contains a plane curve. We prove that the degree of such surfaces is bounded and for $s=4$ we compute an actual bound.
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On smooth surfaces in projective four-space lying on quartic hypersurfaces with isolated singularities
We prove that a smooth surface, non of general type, in projective four-space, which lies on a quartic hypersurface with isolated singularities has degree at most 27 (in fact we prove a slightly more general result).
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Gonality, Clifford index and multisecants
We show, among other things, that in most cases the gonality of a subcanonical curve in projective-three space is computable by multisecants.
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Le probleme de Brill-Noether pour les fibre's de Steiner et application aux courbes gauches
A Steiner bundle over the projective 3-space is the kernel in a trivial bundle of a morphism defined by a matrix of linear forms. We produce various Steiner bundles E of rank n such that E(1) has n-1 sections, the dependency locus of which is a smooth curve.
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