On the tautological ring of $\M _g$

Abstract

We prove among other things that any product of tautological classes of $\M_g$ of degree $d$ (in the Chow ring of $\M _g$ with rational coefficients) vanishes for $d>g-2$ and is proportional to the class of the hyperelliptic locus in degree $g-2$.

6 pages, amstex 2.1

Cited by in corpus (84)

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• The Gorenstein conjecture fails for the tautological ring of ${\bar{\mathcal{M}}}_{2,n}$
• Relations in the tautological ring of the moduli space of curves
• Tautological and non-tautological cohomology of the moduli space of curves
• Topological recursive relations in $H^{2g}(M_{g,n})$
• Irreducibility of Hurwitz spaces
• Relations among tautological classes revisited
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• A vanishing theorem for tautological classes of aspherical manifolds
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• A new proof of Faber's intersection number conjecture
• The class of the locus of intermediate Jacobians of cubic threefolds
• Tautological relations via r-spin structures
• Tautological rings for high dimensional manifolds
• Structure of the mapping class groups of surfaces: a survey and a prospect
• Calculating intersection numbers on moduli spaces of pointed curves
• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)
• Relations in the tautological ring of $M_g$
• The Chow rings of the moduli spaces of curves of genus 7, 8, and 9
• Mapping Class Groups and Moduli Spaces of Curves
• Cohomology of moduli spaces
• Affine geometry of strata of differentials
• Relations among characteristic classes of manifold bundles
• Powers of the theta divisor and relations in the tautological ring
• Computing top intersections in the tautological ring of $M_g$
• Descendent integrals and tautological rings of moduli spaces of curves
• Gerby Localization, Z_3-Hodge Integrals and the GW Theory of C^3/Z_3
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• On the tautological rings of M_{g, 1} and its universal Jacobian
• Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
• The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces
• Generating Functions for Hurwitz-Hodge Integrals
• Topological recursion relations from Pixton's formula
• Algebraic structures on the topology of moduli spaces of curves and maps
• Invariance of tautological equations I: conjectures and applications
• A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
• The pullback of a theta divisor to M_{g,n}
• Extremality of loci of hyperelliptic curves with marked Weierstrass points
• On the cohomological dimension of the moduli space of Riemann surfaces
• The tautological ring of ${\mathcal{M}}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relations
• The local Gromov-Witten theory of curves
• Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes
• The kappa classes on the moduli spaces of curves
• Polynomial families of tautological classes on ${\mathcal{M}}_{g,n}^{rt}$
• A conjectural connection between R^*(C_g^n) and R^*(M_{g,n}^rt)
• Weight two compactly supported cohomology of moduli spaces of curves
• The tautological ring of the moduli space M_{2,n}^rt
• Canonical metric on the space of symplectic invariant tensors and its applications
• Moduli spaces of Riemann surfaces as Hurwitz spaces
• The moduli space of curves and its invariants
• A perfect stratification of M_g for g at most 5
• Tautological classes of definite 4-manifolds
• Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. II
• Poincaré duality of wonderful compactifications and tautological rings
• A vanishing result for tautological classes on the moduli of K3 surfaces
• Cycles on curves and Jacobians: a tale of two tautological rings
• A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces
• Real normalized differentials and compact cycles in the moduli space of curves
• Evaluating tautological classes using only Hurwitz numbers
• Tautological classes with twisted coefficients
• Relative maps and tautological classes
• Symplectic sums and Gromov-Witten invariants
• Tautological ring of strata of differentials
• Real normalized differentials and Arbarello's conjecture
• The Chow ring of the moduli space of curves of genus 6
• A proof of the Faber intersection number conjecture
• Relations on Mbar_{g,n} via orbifold stable maps
• Rings of tautological forms on moduli spaces of curves
• New properties of the intersection numbers on moduli spaces of curves
• Complete subvarieties of moduli spaces and the Prym map
• On the tautological ring of ${\bar{M}}_{g,n}$
• Tautological rings and stabilisation
• Rational cohomology of ${\mathcal{M}}_{4,1}$
• The Chow rings of moduli spaces of elliptic surfaces over ${\mathbb{P}}^1$
• Relations in the Tautological Ring of the Universal Curve
• Complete descriptions of the tautological rings of the moduli spaces of curves of genus lower or equal to 4 with marked points
• Curves of given $p$-rank with trivial automorphism group
• Tautological pairings on moduli spaces of curves
• There are no projective surfaces in M_4
• The p-torsion of curves with large p-rank