A perfect stratification of $${\mathcal M_g}$$ for g ≤ 5

Abstract

We find for g ≤ 5 a stratification of depth g − 2 of the moduli space of curves \({\mathcal M_g}\) with the property that its strata are affine and the classes of their closures provide a \({\mathbb{Q}}\)-basis for the Chow ring of \({\mathcal M_g}\). The first property confirms a conjecture of one of us. The way we establish the second property yields new (and simpler) proofs of theorems of Faber and Izadi which, taken together, amount to the statement that in this range the Chow ring is generated by the λ-class.