On the string-theoretic Euler number of 3-dimensional A-D-E singularities

Abstract

\noindent The stringtheoretic Efunctions Estr(X;u,v) of normal complex varieties X having at most logterminal singularities are defined by means of sncresolutions. We give a direct computation of them in the case in which X is the underlying space of the threedimensional A-D-E singularities by making use of a canonical resolution process. Moreover, we compute the string-theoretic Euler number for several compact complex threefolds with prescribed A-D-E singularities.