Let Fi h(k, n) be the ith ordered configuration space of all distinct points H1, . . . ,Hh in the Grassmannian Gr(k, n) of k-dimensional sub-spaces of Cn, whose sum is a subspace of dimension i. We prove that Fi h(k, n) is (when non empty) a complex submanifold of Gr(k, n)h of dimension i(n - i)...

Let Fi h(k, n) be the ith ordered configuration space of all distinct points H1, . . . ,Hh in the Grassmannian Gr(k, n) of k-dimensional sub- spaces of Cn, whose sum is a subspace of dimension i. We prove that Fi h(k, n) is (when non empty) a complex submanifold of Gr(k, n)h of dimension i(n -...

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper we prove that if TfW is the toric arrangement defined by the cocharacters lattice of a Weyl group fW, then the integer cohomology of its complement is...

Here the reader can find some basic definitions and notations in order to better understand the model for social choise described by L. Marengo and S. Settepanella in their paper: Social choice among complex objects. The interested reader can refer to [Bou68], [Massey] and [OT92] to go into more...

The paper presents a new framework to assess firm level heterogeneity and to study the rate and direction of technical change. Building on the analysis of revealed short-run production functions by Hildenbrand (1981), we propose the (normalized) volume of the zonotope composed by vectors-firms...

Recently, Marengo and Settepanella (2010) introduced a model of social choice among bundles of interdependent elements. In this paper we prove that their voting model is highly decidable, i.e. a group of agents that agrees to use such voting process has an high probability to reach a final...

In [MP08] L. Marengo and C. Pasquali present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained. In this paper we extend and generalize this approach by providing a geometric model of...

Suppose R is the complement of an essential arrangement of toric hyperlanes in the complex torus (C*)n and pi = pi1(R). We show that H*(R; A) vanishes except in the top degree n when A is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex...

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper we build a CW-complex S homotopy equivalent to the arrangement complement Rx, with a combinatorial description similar to that of the well-known...