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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)
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)