Let Mg;n denote the moduli space of genus g stable algebraic curves with n marked points. It carries the Mumford cohomology classes κi. A homology class in H*(Mg;n) is said to be κ-zero if the integral of any monomial in the κ-classes vanishes on it. We show that any κ-zero class implies a partial differential equation for generating series for certain intersection indices on the moduli spaces. The genus homogeneous components of the Witten-Kontsevich potential, as well as of the more general Hodge potential, which include, in addition to Ψ-classes, intersection indices for λ-classes, are special cases of these generating series, and the well-known partial differential equations for them are instances of our general construction.
|Number of pages||15|
|Journal||Moscow Mathematical Journal|
|Publication status||Published - 2012|
- Deligne-Mumford compactification
- Hodge integrals
- Moduli spaces
- Witten-Kontsevich potential