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In the present paper, we revisit the geometry of smooth plane quartics and their bitangents from several perspectives. First, we study in detail the weak combinatorics of arrangements of bitangents associated with highly symmetric quartic curves. We consider quartic curves from the point of view of the order of their automorphism groups, in order to establish a lower bound on the number of quadruple intersection points for arrangements of bitangents associated with smooth plane quartics, which are smooth members of Ciani's pencil. We then construct new examples of $3$-syzygy reduced plane curves using smooth plane quartics and their bitangents., Comment: 20 pages, this is the final version, to appear in Fundamenta Mathematicae

The main purpose of this paper is to provide combinatorial constraints on the constructability of free and nearly free arrangements of smooth plane conics admitting certain ${\rm ADE}$ singularites., Comment: 13 pages, this is the final version, including the referee's comments, to be published in Annali dell'Universit\`a di Ferrara (EDGE Volume 2018 - 2022)

In the present paper, we study conic-line arrangements having nodes, tacnodes, and ordinary triple points as singularities. We provide combinatorial constraints on such arrangements and we give the complete classification of free arrangements in this class., Comment: 24 pages, 2 figures, a minor revision incorporating referee's remarks

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study $3$-syzygy arrangements and we present examples that admit unexpected curves., Comment: 19 pages, one figure, version after referee's remarks