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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Obstructions and hypersurface sections (minimally elliptic singularities)

Authors: Kurt Behnke and Jan Arthur Christophersen
Journal: Trans. Amer. Math. Soc. 335 (1993), 175-193
MSC: Primary 14J17; Secondary 14B07
MathSciNet review: 1069742
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Abstract: We study the obstruction space $ {T^2}$ for minimally elliptic surface singularities. We apply the main lemma of our previous paper [3] which relates $ {T^2}$ to deformations of hypersurface sections. To use this we classify general hypersurface sections of minimally elliptic singularities. As in the rational singularity case there is a simple formula for the minimal number of generators for $ {T^2}$ as a module over the local ring. This number is in many cases (e.g. for cusps of Hilbert modular surfaces) equal to the vector space dimension of $ {T^2}$.

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Keywords: Deformations of singularities, obstructions, hypersurface section, minimally elliptic singularities, degeneration of the tangent cone
Article copyright: © Copyright 1993 American Mathematical Society