Tautological Pairings on Moduli Spaces of Curves
نویسندگان
چکیده
We 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 Poincaré duality. The structure of the tautological ring of the moduli space of stable curves is predicted by the Faber conjecture, which states that R(Mg,n) is Gorenstein with socle in dimension 3g−3+n = dimMg,n. We break this statement into two parts: Socle: The tautological ring vanishes in high degree and it is onedimensional in top degree.
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