Singular locus of an infinite integral extension (Q1178899)

The main object of this paper is to construct an example of a normal noetherian pseudo-geometric surface which is locally, but not globally, excellent \((*)\). The authors consider in the rational plane an infinite union of horizontal and vertical lines defined by \(X=a_ i\) and \(Y=b_ i\). In the infinite dimensional space with coordinates \((X,Y,T_ 1,T_ 2,\dots)\) let us define the surface \(G\) given by the equations \(T_ i^{d_ i}=(X-a_ i)(Y-b_ i)\). This is an infinite abelian covering of the plane. When the infinite sequence of points \((a_ i,b_ i)\) is siutably chosen this covering satisfies \((*)\).