On the closure in $\overline M_g$ of smooth curves having a special Weierstrass point

Abstract

Let $\overline{wt(2)}$ be the closure in $\overline M_g$, the coarse moduli space of stable complex curves of genus $g \ge 3$, of the locus in $M_g$ of curves possessing a Weierstrass point of weight at least 2. The class of $\overline{wt(2)}$ in the group Pic($\overline M_g)\otimes \boldsymbol Q$ is computed. The computation heavily relies on the notion of "derivative" of a relative Wronskian, introduced in [15] for families of smooth curves and here extended to suitable families of Deligne-Mumford stable curves. Such a computation provides, as a byproduct, a simpler proof of the main result proven in [6].