Nickolas Michelacakis

A Comment on 'Cross-Border Merger, Vertical Structure, and Spatial Competition'

The aim of this paper is to revise and correct the results obtained in Beladi et al. [Beladi, H., Chakrabarti, A., Marjit, S., 2010. Cross-border merger, vertical structure, and spatial competition. Economics Letters 109, 112-114]. Specifically, we prove that the Nash equilibrium locations of the downstream firms are the same in the pre-merger free-trade case as they are following a cross-border upstream merger.

Projective flat manifolds of cyclic and dihedral holonomy

In this note, we classify the projective flat manifolds whose holonomy group is either a cyclic group C(p) or dihedral D(2p), with p prime. We give an estimate for the size of the set of their positive line bundles and construct explicitly and directly in terms of the representation space of the holonomy group some interesting imbeddings.

On the Picard group of a compact flat projective variety

In this note, we describe the Picard group of the class of compact, smooth, flat, projective varieties. In view of Charlaps work and Johnsons characterization, we construct line bundles over such manifolds as the holonomy-invariant elements of the Neron-Severi group of a projective flat torus covering the manifold. We prove a generalized version of the Appell-Humbert theorem which shows that the nontrivial elements of the Picard group are precisely those coming from the above construction. our calculations finally give an estimate for the set of positive line bundles for such varieties.