location:  Publications → journals → CMB
Abstract view

# 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 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

 top of page | contact us | privacy | site map |