Journal of the Mathematical Society of Japan

Surface singularities on cyclic coverings and an inequality for the signature

Tadashi ASHIKAGA

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Abstract

For the signature of the Milnor fiber of a surface singularity of cyclic type, we prove a certain inequality, which naturally induce an answer of Durfee's conjecture in this case. For the proof, we use a certain perturbation method on the way of Hirzebruch's resolution process.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 2 (1999), 485-521.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108029

Digital Object Identifier
doi:10.2969/jmsj/05120485

Mathematical Reviews number (MathSciNet)
MR1674761

Zentralblatt MATH identifier
0956.14024

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 14H20: Singularities, local rings [See also 13Hxx, 14B05] 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 32S25: Surface and hypersurface singularities [See also 14J17]

Keywords
Signature Milnor fiber cyclic covering plane curve singularity geometric genus Milnor number

Citation

ASHIKAGA, Tadashi. Surface singularities on cyclic coverings and an inequality for the signature. J. Math. Soc. Japan 51 (1999), no. 2, 485--521. doi:10.2969/jmsj/05120485. https://projecteuclid.org/euclid.jmsj/1213108029


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