The Euler number of the normalization of an algebraic threefold with ordinary singularities

Shoji Tsuboi. "The Euler number of the normalization of an algebraic threefold with ordinary singularities." Banach Center Publications 65.1 (2004): 273-289. <http://eudml.org/doc/282525>.

@article{ShojiTsuboi2004,
abstract = {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) $D_S$ 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).},
author = {Shoji Tsuboi},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {273-289},
title = {The Euler number of the normalization of an algebraic threefold with ordinary singularities},
url = {http://eudml.org/doc/282525},
volume = {65},
year = {2004},
}

TY - JOUR
AU - Shoji Tsuboi
TI - The Euler number of the normalization of an algebraic threefold with ordinary singularities
JO - Banach Center Publications
PY - 2004
VL - 65
IS - 1
SP - 273
EP - 289
AB - 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) $D_S$ 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).
LA - eng
UR - http://eudml.org/doc/282525
ER -