The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the $\kappa$ classes on the moduli space of nonsingular genus $g$ curves. In a series of steps, the stable quotient relations are rewritten in successively simpler forms. The final result is the proof of the Faber–Zagier relations (conjectured in 2000).

中文翻译：

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曲线模空间的重言环中的关系

稳定商数模空间的虚拟几何用于获得非奇异类$ g $曲线的模空间上$ \ kappa $类之间的Chow关系。在一系列步骤中，稳定的商关系以连续简单的形式重写。最终结果是Faber-Zagier关系的证明（推测于2000年）。