Illinois Journal of Mathematics

Cohomology of ideals in elliptic surface singularities

Tomohiro Okuma

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Abstract

We introduce the the normal reduction number of two-dimensional normal singularities and prove that elliptic singularity has normal reduction number two. We also prove that for a two-dimensional normal singularity which is not rational, it is Gorenstein and its maximal ideal is a $p_{g}$-ideal if and only if it is a maximally elliptic singularity of degree $1$.

Article information

Source
Illinois J. Math., Volume 61, Number 3-4 (2017), 259-273.

Dates
Received: 12 October 2016
Revised: 13 January 2018
First available in Project Euclid: 22 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1534924827

Digital Object Identifier
doi:10.1215/ijm/1534924827

Mathematical Reviews number (MathSciNet)
MR3845721

Zentralblatt MATH identifier
06932504

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Citation

Okuma, Tomohiro. Cohomology of ideals in elliptic surface singularities. Illinois J. Math. 61 (2017), no. 3-4, 259--273. doi:10.1215/ijm/1534924827. https://projecteuclid.org/euclid.ijm/1534924827


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