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We prove that the moduli space $\mathcal{M}_g$ of smooth curves of genus $g$is the union of $g-1$ affine open subsets for every $g$ with $2 \le g \le 5$,as predicted by an intriguing conjecture of Eduard Looijenga.

An affine open covering of $\mathcal{M}_g$ for $g \le 5$