The Euler number of the normalization of an algebraic threefold with ordinary singularities
Tom 65 / 2004
Banach Center Publications 65 (2004), 273-289
MSC: Primary 32S20; Secondary 32S25, 14C17, 14C21.
DOI: 10.4064/bc65-0-17
Streszczenie
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).
