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

• Volume: 65, Issue: 1, page 273-289
• ISSN: 0137-6934

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## Abstract

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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).

## How to cite

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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 -

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