Syzygies and logarithmic vector fields along plane curves
By Alexandru Dimca, E. Sernesi. 2014
71 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ab28b416d5051765393199dbc049af02efdd3e92
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In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Freeness versus maximal global Tjurina number for plane curves (2015, methodology): “1) d1 + d2 = d− 1 and τ(C) = (d− 1)(2) − d1d2, where τ(C) is the total Tjurina number of C, see for instance [4], [5].”