Tohoku Mathematical Journal

On the defining equations of hypersurface purely elliptic singularities

Naohiro Kanesaka

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Abstract

We investigate a class of isolated hypersurface singularities, the so-called purely elliptic singularities, of complex algebraic varieties of dimension greater than or equal to two. We show that, for hypersurface purely elliptic singularities defined by nondegenerate polynomials, Calabi-Yau varieties arising among the irreducible components of the essential divisors are concretely associated with the defining equations of these singularities, and that the birational class of the Calabi-Yau varieties does not depend on the irreducible components.

Article information

Source
Tohoku Math. J. (2), Volume 57, Number 1 (2005), 1-10.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113234830

Digital Object Identifier
doi:10.2748/tmj/1113234830

Mathematical Reviews number (MathSciNet)
MR2113986

Zentralblatt MATH identifier
1081.32019

Subjects
Primary: 32S25: Surface and hypersurface singularities [See also 14J17]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Citation

Kanesaka, Naohiro. On the defining equations of hypersurface purely elliptic singularities. Tohoku Math. J. (2) 57 (2005), no. 1, 1--10. doi:10.2748/tmj/1113234830. https://projecteuclid.org/euclid.tmj/1113234830


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