منابع مشابه
Recursion Formulae of Higher Weil-petersson Volumes
Abstract. In this paper we study effective recursion formulae for computing intersection numbers of mixed ψ and κ classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani’s recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the...
متن کاملHigher Weil-petersson Volumes and Tautological Constants
We prove in this paper an effective recursion formula for all intersection numbers of mixed ψ and κ classes on moduli spaces of curves. Several related general recursive formulas are also proved. Some of these formulas contain certain tautological constants, which are given by the secant Euler numbers and series expansion of Bessel functions of the first kind.
متن کاملWeil-petersson Volumes and Cone Surfaces
The moduli spaces of hyperbolic surfaces of genus g with n geodesic boundary components are naturally symplectic manifolds. Mirzakhani proved that their volumes are polynomials in the lengths of the boundaries by computing the volumes recursively. In this paper we give new recursion relations between the volume polynomials.
متن کاملEstimates of Weil-petersson Volumes via Effective Divisors
The Mumford class κ1 on Mg,0 was shown to be proportional to the cohomology class [ωWP ] of the Weil-Petersson form by Wolpert in [WO]. Furthermore he showed that the restriction of this class to any component of the compactyfying divisor coincides with the corresponding Weil-Petersson class. Arbarello and Cornalba introduced classes κ1 on Mg,n, proved a similar restriction property for these a...
متن کاملOn the Large Genus Asymptotics of Weil-petersson Volumes
A relatively fast algorithm for evaluatingWeil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the Weil-Petersson volumes is computed. Asymptotic formulas for the intersection numbers involving ψ-classes are conjectured as well. The precision of the formulas is high enough to believe that they a...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1992
ISSN: 0022-040X
DOI: 10.4310/jdg/1214448257