On the closure in M̄g of smooth curves having a special Weierstrass point

Let wt(2) be the closure in M̄g, the coarse moduli space of stable complex curves of genus g ≥ 3, of the locus in M̄g of curves possessing a Weierstrass point of weight at least 2. The class of wt(2) in the group Pic(M̄g) ⊗ 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].