In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods , such as the enumeration of the graphs involved in a suitable stratification of M 2,n .
We determine the structure of the *-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra bundle, and turns out to be a product of sl(4, C) with the full special linear superalgebras of some graded vector spaces… (More)
In this paper we deal with the action of the symmetric group on the cohomology of the configuration space Cn(d) of n points in R d. This topic has been studied by several authors, e. 1 and, for d odd, H * (Cn(d); C) ∼ = CSn. On the cohomology algebra H * (Cn(d); C) there is, in addition to the natural Sn-action, an extended action of Sn+1; this was first… (More)
Given an orientable weakly self-dual manifold X of rank two, we build a geometric realization of the Lie algebra sl(6, C) as a naturally defined algebra L C of endomorphisms of the space of differential forms of X. We provide an explicit description of Serre generators in terms of natural generators of L C. This construction gives a bundle on X which is… (More)
We study the general properties of rank two s-Kähler manifolds. We present several natural examples of manifolds which can be equipped with this structure with various levels of rigidity: complex tori and abelian varieties, cotangent bundles of smooth manifolds and moduli of pointed elliptic curves. We show how one can obtain natural bundles of Lie algebras… (More)