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arXiv · 1401.6838

Syzygies and logarithmic vector fields along plane curves

Alexandru Dimca·Edoardo Sernesi
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Abstract

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.

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Alexandru Dimca, Edoardo Sernesi. 2014-05-03. Syzygies and logarithmic vector fields along plane curves. https://arxiv.org/abs/1401.6838

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