Displaying similar documents to “Intersection theory on Deligne-Mumford compactifications”

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

Rolf-Peter, Holzapfel (1997)

Serdica Mathematical Journal

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We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs...

Invertible cohomological field theories and Weil-Petersson volumes

Yuri I. Manin, Peter Zograf (2000)

Annales de l'institut Fourier

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We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....