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

• Autorzy: Shoji Tsuboi
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 14C21: Pencils, nets, webs
• 32S20: Global theory of singularities; cohomological properties
• 14C17: Intersection theory, characteristic classes, intersection multiplicities
• 32S25: Surface and hypersurface singularities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 65
• Numer: 1
• Strony: 273-289

Daty

wydano

2004

Twórcy

autor

Shoji Tsuboi

• Department of Mathematics and Computer Science, Kagoshima University, Kourimoto 1-21-35, 890-0065 Kagoshima, Japan

Identyfikatory

DOI

10.4064/bc65-0-17