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Aramayona and Leininger have provided a "finite rigid subset"$\mathfrak{X}(\Sigma)$ of the curve complex $\mathscr{C}(\Sigma)$ of a surface$\Sigma = \Sigma^n_g$, characterized by the fact that any simplicial injection$\mathfrak{X}(\Sigma) \to \mathscr{C}(\Sigma)$ is induced by a unique elementof the mapping class group $\mathrm{Mod}(\Sigma)$. In this paper we prove that,in the case of the sphere with $n\geq 5$ marked points, the reduced homologyclass of the finite rigid set of Aramayona and Leininger is a$\mathrm{Mod}(\Sigma)$-module generator for the reduced homology of the curvecomplex $\mathscr{C}(\Sigma)$, answering in the affirmative a question posed byAramayona and Leininger. For the surface $\Sigma = \Sigma_g^n$ with $g\geq 3$and $n\in \{0,1\}$ we find that the finite rigid set $\mathfrak{X}(\Sigma)$ ofAramayona and Leininger contains a proper subcomplex $X(\Sigma)$ whose reducedhomology class is a $\mathrm{Mod}(\Sigma)$-module generator for the reducedhomology of $\mathscr{C}(\Sigma)$ but which is not itself rigid.

Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface