Integrals of psi-classes over double ramification cycles

Abstract

DR-cycles are certain cycles on the moduli space of curves. Intuitively, they parametrize curves that allow a map to \mathbb{P}^1 with some specified ramification profile over two points. They are known to be tautological classes, but in general there is no known expression in terms of standard tautological classes. In this paper, we compute the intersection numbers of those DR-cycles with any monomials in psi-classes when this intersection is zero-dimensional.

43 pages

References in corpus (2)

• Normal Functions and the Geometry of Moduli Spaces of Curves
• Gromov-Witten invariants of target curves via Symplectic Field Theory

Cited by in corpus (23)

• Double ramification cycles on the moduli spaces of curves
• Double ramification cycles and integrable hierarchies
• Holomorphic anomaly equations and the Igusa cusp form conjecture
• Tau-structure for the Double Ramification Hierarchies
• Double ramification cycles with target varieties
• Integrable systems of double ramification type
• DR/DZ equivalence conjecture and tautological relations
• Flat F-manifolds, F-CohFTs, and integrable hierarchies
• Cohomology classes of strata of differentials
• Quadratic double ramification integrals and the noncommutative KdV hierarchy
• Integrability, Quantization and Moduli Spaces of Curves
• Towards a bihamiltonian structure for the double ramification hierarchy
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• The quantum Witten-Kontsevich series and one-part double Hurwitz numbers
• Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture
• A conjectural formula for $D{R}_g(a,-a){\lambda }_g$
• On the spectral problem of the quantum KdV hierarchy
• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
• Moduli spaces of residueless meromorphic differentials and the KP hierarchy
• A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy
• Quantum KdV hierarchy and shifted symmetric functions
• Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve
• Integrable systems of finite type from F-cohomological field theories without unit