We compute the integral Chow rings of M̄1,n for $n=3,4$. For n≤ 6, these stacks can be obtained by a sequence of weighted blow-ups and blow-downs from a simple stack, either a weighted projective space or a Grassmannian. Our strategy consists in inductively computing all the integral Chow rings of the alternative compactifications introduced by Smyth and studied by Lekili-Polishchuk.
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Battistella et al. (2024) studied this question.
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