4 problems

Let $C$ be a reduced plane curve in $cmathbb{P}^2$. A point $p\in C$ is modular if the central projection from $p$ induces a locally trivial fibration of the complement…

Let $C=V(f)$ be a reduced $3$-syzygy plane curve, meaning that it has a first syzygy matrix $M_f$ that is a square matrix of size $3$. Let $p\in\operatorname{Sing}(C)$ be an isolat…

Let $C$ be a rational cuspidal plane curve, meaning a rational curve in $cmathbb{P}^2$ with only unibranch singularities. Freeness conjecture. Every such curve $C$ is either free o…

Let $\mathcal C$ be a rational cuspidal curve in the plane. Here, rational means that $\mathcal C$ has genus zero, and cuspidal means that all its singularities are cusps. Freeness…