Cohomology algebra of plane curves, weak combinatorial type, and formality (Q2844729)

The weak combinatorial type of a plane curve \(C\) consists of the following data: the number of irreducible components of \(C\), with their degrees and genera, the number of local branches of each component at every singularity of \(C\), and the intersection numbers of every two such local branches. The authors show that the cohomology algebra of the complement \(S_C\) of \(C\) is determined by the above weak combinatorial type. As corollaries, they show that \(S_C\) is a formal space in the sense of Sullivan and that the irreducible components of the rank \(1\) twisted cohomology jumping loci of \(S_C\) passing through the origin are determined by the weak combinatorial type of the plane curve \(C\).