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On Hodge Theory of Singular Plane Curves

Published online by Cambridge University Press:  20 November 2018

Nancy Abdallah
Nancy Abdallah*
Affiliation:
Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France e-mail: nancy.n.abdallah@gmail.com
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Abstract

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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 ${{H}^{2}}\left( U,\,\mathbb{C} \right)$.

Keywords

32S3532S2214H50plane curvesHodge and pole order filtrations
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 449 - 460
Copyright
Copyright © Canadian Mathematical Society 2016

References

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