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On Hodge Theory of Singular Plane Curves

  Published:2016-05-25
 Printed: Sep 2016
  • Nancy Abdallah,
    Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
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Abstract

The dimensions of the graded quotients of the cohomology of a plane curve complement $U=\mathbb P^2 \setminus C$ 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 $H^2(U,\mathbb C)$.
Keywords: plane curves, Hodge and pole order filtrations plane curves, Hodge and pole order filtrations
MSC Classifications: 32S35, 32S22, 14H50 show english descriptions Mixed Hodge theory of singular varieties [See also 14C30, 14D07]
Relations with arrangements of hyperplanes [See also 52C35]
Plane and space curves
32S35 - Mixed Hodge theory of singular varieties [See also 14C30, 14D07]
32S22 - Relations with arrangements of hyperplanes [See also 52C35]
14H50 - Plane and space curves
 

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