Integral Chow rings of modular compactifications of ℳ1,𝑛≤6

For 𝑛≤6, we compute the integral Chow ring of every modular compactification of ℳ1,𝑛 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, we study whether Getzler’s relation holds integrally and for other compactifications.