Linear sections of the Severi variety and moduli of curves -- Maksym Fedorchuk

In this talk, we discuss the geometry of the Severi variety of plane curves of degree $d$ and genus $g$, and the associated moduli map to the coarse moduli space $\bar{M}_g$ of stable curves of genus $g$. The one-dimensional linear sections of the Severi variety induce curves in $\bar{M}_g$, which are free once $d$ is large enough. We will explain how the degeneration techniques can be applied to study the geometry and numerical invariants of these curves.