Tohoku Mathematical Journal
2005

March
SECOND SERIES VOL. 57, NO. 1

Tohoku Math. J.
57 (2005), 1-10

Title ON THE DEFINING EQUATIONS OF HYPERSURFACE PURELY ELLIPTIC SINGULARITIES

Author Naohiro Kanesaka

(Received January 25, 2001, revised May 6, 2004)
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.

2000 Mathematics Subject Classification. Primary 32S25; Secondary 14B05, 14M25.

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