On Hodge Theory of Singular Plane Curves
Nancy Abdallah (JAD)
TL;DR
This paper explores the Hodge theory of singular plane curves, relating the cohomology of their complements to geometric invariants, especially focusing on curves with ordinary singularities.
Contribution
It provides a detailed description of the Hodge filtration dimensions for plane curve complements, linking them to simple geometric invariants and analyzing curves with ordinary singularities.
Findings
Dimensions of Hodge filtration quotients are expressed via geometric invariants.
Detailed analysis of curves with ordinary singularities.
Connections between cohomology and geometry are established.
Abstract
The dimensions of the graded quotients of the cohomology of a plane curve complement 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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology