The codimension-two homology of the moduli space of stable curves is algebraic (Q1196406)

Let \({\mathcal M}_ g\) be the moduli space of stable curves of genus \(g\). The author first finds \(a={[(g^ 2-1)/4]}+3g-3\) generators for the Chow group \(A^ i_ \mathbb{Q}(\overline{{\mathcal M}}_ g-{\mathcal M}_ g)\) and uses this fact to show that \(a\) is an upper bound on the rank of the homology group \(H_{2(3g-3)-4}(\overline {\mathcal M}_ g-{\mathcal M}_ g,\mathbb{Q})\). The dual basis for \(H_ 4(\overline{\mathcal M}_ g)\) is seen to be algebraic.