Obstructions and hypersurface sections (minimally elliptic singularities)

Behnke, Kurt; Christophersen, Jan Arthur

doi:10.1090/S0002-9947-1993-1069742-2

Obstructions and hypersurface sections (minimally elliptic singularities)
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by Kurt Behnke and Jan Arthur Christophersen PDF

Trans. Amer. Math. Soc. 335 (1993), 175-193 Request permission

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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