Geodesic
On Hodge Theory of Singular Plane Curves
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 449-460

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DOI

The dimensions of the graded quotients of the cohomology of a plane curve complement $U\,=\,{{\mathbb{P}}^{2}}\,\backslash \,C$ with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration on ${{H}^{2}}\left( U,\,\mathbb{C} \right)$ .
DOI : 10.4153/CMB-2016-010-4
Mots-clés : 32S35, 32S22, 14H50, plane curves, Hodge and pole order filtrations 
Abdallah, Nancy. On Hodge Theory of Singular Plane Curves. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 449-460. doi: 10.4153/CMB-2016-010-4
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     author = {Abdallah, Nancy},
     title = {On {Hodge} {Theory} of {Singular} {Plane} {Curves}},
     journal = {Canadian mathematical bulletin},
     pages = {449--460},
     year = {2016},
     volume = {59},
     number = {3},
     doi = {10.4153/CMB-2016-010-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-010-4/}
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