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Abstract

By a classical formula due to Enriques, the Euler number $\chi(X)$ of the non-singular normalization $X$ of an algebraic surface $S$ with ordinary singularities in $ P^3(\mathbb C)$ is given by $\chi(X)=n(n^2-4n+6)-(3n-8)m+3t-2\gamma$, where $n$ is the degree of $S$, $m$ the degree of the double curve (singular locus) $D_S$ of $S$, $t$ is the cardinal number of the triple points of $S$, and $\gamma$ the cardinal number of the cuspidal points of $S$. In this article we shall give a similar formula for an algebraic threefold with ordinary singularities in $ P^4(\mathbb C)$ which is free from quadruple points (Theorem 4.1).