Abstract
We describe in simple geometric terms the Hodge filtration on the cohomology $H^*(U)$ of the complement $U=\mathsf{P}^2 \setminus C$ of a plane curve $C$ with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal and pole order filtration on $H^2(U)$ are given.
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