Poincaré duality of wonderful compactifications and tautological rings

Abstract

Let $g\ge 2$. Let $M_{g,n}^{rt}$ be the moduli space of $n$-pointed genus $g$ curves with rational tails. Let $C_g^n$ be the $n$-fold fibered power of the universal curve over $M_g$. We prove that the tautological ring of $M_{g,n}^{rt}$ has Poincaré duality if and only if the same holds for the tautological ring of $C_g^n$. We also obtain a presentation of the tautological ring of $M_{g,n}^{rt}$ as an algebra over the tautological ring of $C_g^n$. This proves a conjecture of Tavakol. Our results are valid in the more general setting of wonderful compactifications.

11 pages. v2: Removed the incorrect Proposition 2.14, some other improvements and corrected inaccuracies. Final version, to appear in IMRN

References in corpus (4)

• Three questions in Gromov-Witten theory
• A conjectural connection between R^*(C_g^n) and R^*(M_{g,n}^rt)
• The Chow ring of a Fulton-MacPherson compactification
• Cycles on curves and Jacobians: a tale of two tautological rings

Cited by in corpus (1)

• The Chow ring of a Fulton-MacPherson compactification