2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221445We discuss analogs of Faber's conjecture for two nested sequences of partial compactifications of the moduli space of smooth curves. We show that their tautological rings are one-dimensional in top degree but do not satisfy Poincare duality.Algebraic Geometry14H10Tautological pairings on moduli spaces of curvestext