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

Banach Center Publications (2004)

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

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topShoji 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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