In this paper, we present a solution to the problem of the analytic classification of germs of plane curves with several irreducible components. Our algebraic approach follows precursive ideas of Oscar Zariski and as a subproduct allows us to recover some particular cases found in the literature.

We study plane curves over finite fields whose tangent lines at smooth $\mathbb {F}_q$-points together cover all the points of $\mathbb {P}^2(\mathbb {F}_q)$.

Using recent results by Măcinic, Papadima and Popescu, and a refinement of an older construction of ours, we determine the monodromy action on $H^{1}(F(G),\mathbb{C})$, where $F(G)$ denotes the Milnor fiber of a hyperplane arrangement associated to an irreducible complex reflection group $G$.

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

In this work, we describe a method to construct the generic braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting since it combines two techniques, namely, the construction of a highly non-generic braid monodromy and a systematic method to go from a non-generic to a generic braid monodromy. The latter process, called generification, is independent from Kummer covers, and it can be applied in more general circumstances since non-generic braid monodromies appear more naturally and are oftentimes much easier to compute. Explicit examples are computed using these techniques.