Tautological relations in moduli spaces of weighted pointed curves

Abstract

Pandharipande-Pixton have used the geometry of the moduli space of stable quotients to produce relations between tautological Chow classes on the moduli space $M_g$ of smooth genus g curves. We study a natural extension of their methods to the boundary and more generally to Hassett's moduli spaces ${\overline{M}}_{g,w}$ of stable nodal curves with weighted marked points. Algebraic manipulation of these relations brings them into a Faber-Zagier type form. We show that they give Pixton's generalized FZ relations when all weights are one. As a special case, we give a formulation of FZ relations for the n-fold product of the universal curve over $M_g$.

Part of author's PhD thesis, proof of Pixton's relations superseded by arXiv:1509.08421, 31 pages, 1 figure, v2: various corrections

References in corpus (6)

• Relations in the tautological ring of the moduli space of curves
• Relations in the tautological ring
• Conjectural relations in the tautological ring of ${\bar{M}}_{g,n}$
• Relations on Mbar_{g,n} via 3-spin structures
• Relations in the tautological ring of $M_g$
• The Chow ring of Mbar_{0,m}(n, d)

Cited by in corpus (9)

• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures
• The moduli space of curves and its invariants
• Cycles on curves and Jacobians: a tale of two tautological rings
• Tautological classes with twisted coefficients
• Poincaré duality of wonderful compactifications and tautological rings
• Relations on Mbar_{g,n} via orbifold stable maps
• Relations in the Tautological Ring of the Universal Curve