An affine open covering of $\mathcal{M}_g$ for $g \le 5$
  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. 
Claudio Fontanari and Stefano Pascolutti
math.AG