Reconstructing curves from their Hodge classes

Maria Gioia Cifani, Gian Pietro Pirola, Enrico Schlesinger

Let $S$ be a smooth algebraic surface in ${\mathbb{P}}^3(\mathbb{C})$. A curve $C$ in $S$ has a cohomology class ${\eta }_C\in H^1\left({\Omega }_S^1\right)$. Define $\alpha (C)$ to be…