Abstract For n ≤ 6 n 6, we compute the integral Chow ring of every modular compactification of M 1, n M₁, ₍ parametrising only Gorenstein curves with smooth, distinct markings. These include the Deligne–Mumford, Schubert, and Smyth compactifications, and many more. They can all be excised from the stack of log-canonically polarised Gorenstein curves. The Chow ring of the latter admits a simple, combinatorial description, which we compute by patching along a natural stratification by core level. We deduce that all these modular compactifications satisfy the Chow–Künneth generation property, that the cycle class map is an isomorphism, and for n = 4 n=4, we study whether Getzler’s relation holds integrally and for other compactifications.
Battistella et al. (Wed,) studied this question.
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