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

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Tsuboi S.

Banach Center Publications

2004

tom 65

nr 1

273-289

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).

Ograniczanie wyników

1 Banach Center Publications

1 Tsuboi S.

1 2004

Wyniki wyszukiwania

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