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Syzygies and logarithmic vector fields along plane curves

Alexandru Dimca, Edoardo Sernesi (2014)

Journal de l’École polytechnique — Mathématiques

We investigate the relations between the syzygies of the Jacobian ideal of the defining equation for a plane curve C and the stability of the sheaf of logarithmic vector fields along C , the freeness of the divisor C and the Torelli properties of C (in the sense of Dolgachev-Kapranov). We show in particular that curves with a small number of nodes and cusps are Torelli in this sense.

The equations of space curves on a quadric.

Roberta Di Gennaro, Uwe Nagel (2007)

Collectanea Mathematica

The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.

The Hilbert Scheme of Buchsbaum space curves

Jan O. Kleppe (2012)

Annales de l’institut Fourier

We consider the Hilbert scheme H ( d , g ) of space curves C with homogeneous ideal I ( C ) : = H * 0 ( C ) and Rao module M : = H * 1 ( C ) . By taking suitable generizations (deformations to a more general curve) C of C , we simplify the minimal free resolution of I ( C ) by e.g making consecutive free summands (ghost-terms) disappear in a free resolution of I ( C ) . Using this for Buchsbaum curves of diameter one ( M v 0 for only one v ), we establish a one-to-one correspondence between the set 𝒮 of irreducible components of H ( d , g ) that contain ( C ) and a set of minimal...

Currently displaying 161 – 180 of 205