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The Hilbert scheme of space curves of small diameter

Jan Oddvar Kleppe (2006)

Annales de l’institut Fourier

This paper studies space curves C of degree d and arithmetic genus g , with homogeneous ideal I and Rao module M = H * 1 ( I ˜ ) , whose main results deal with curves which satisfy 0 Ext R 2 ( M , M ) = 0 (e.g. of diameter, diam M ≤ 2 ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, H ( d , g ) , at ( C ) under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of C turns out to be equivalent to the...

The irregularity of ruled surfaces in three dimensional projective space.

Luis Giraldo, Ignacio Sols (1998)

Collectanea Mathematica

Let S be a ruled surface in P3 with no multiple generators. Let d and q be nonnegative integers. In this paper we determine which pairs (d,q) correspond to the degree and irregularity of a ruled surface, by considering these surfaces as curves in a smooth quadric hypersurface in P5.

Currently displaying 181 – 200 of 205