By a classical formula due to Enriques, the Euler number χ(X) of the non-singular normalization X of an algebraic surface S with ordinary singularities in P³(ℂ) is given by χ(X) = n(n²-4n+6) - (3n-8)m + 3t - 2γ, where n is the degree of S, m the degree of the double curve (singular locus) of S, t is the cardinal number of the triple points of S, and γ 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 P⁴(ℂ) which is free from quadruple points (Theorem 4.1).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-17,
author = {Shoji Tsuboi},
title = {The Euler number of the normalization of an algebraic threefold with ordinary singularities},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {273-289},
zbl = {1072.32021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-17}
}
Shoji Tsuboi. The Euler number of the normalization of an algebraic threefold with ordinary singularities. Banach Center Publications, Tome 65 (2004) pp. 273-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-17/