Affine Stratification of ${\mathcal{A}}_4$

Abstract

We construct an affine stratification for ${\mathcal{A}}_4(\mathbb{C})$ of length 6, in the sense of Roth and Vakil, which gives us an upper bound of 6 for the cohomological dimension of ${\mathcal{A}}_4(\mathbb{C})$. We conjecture that in general for arbitrary $g$ the cohomological dimension of ${\mathcal{A}}_g$ is equal to $g(g-1)/2$.