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Curves on a double surface.

Scott Nollet; Enrico Schlesinger — 2003

Collectanea Mathematica

Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes of locally...

Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$ -space

Robin Hartshorne; Irene Sabadini; Enrico Schlesinger — 2008

Annales de l’institut Fourier

We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of $ℙ^{N}$ is glicci, that is, whether every zero-scheme in $ℙ^{3}$ is glicci. We show that a general set of $n \geq 56$ points in $ℙ^{3}$ admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in $ℙ^{3}$ .

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Curves on a double surface.

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$ -space