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2001•International Journal of MathematicsRequires access

HYPERSURFACE EXCEPTIONAL SINGULARITIES

Shihoko Ishii, Yuri Prokhorov

Open publisher page 26 citations

Abstract

This paper studies hypersurface exceptional singularities in [Formula: see text] defined by non-degenerate function. For each canonical hypersurface singularity, there exists a weighted homogeneous singularity such that the former is exceptional if and only if the latter is exceptional. So we study the weighted homogeneous case and prove that the number of weights of weighted homogeneous exceptional singularities are finite. Then we determine all exceptional singularities of the Brieskorn type of dimension 3.

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What this paper is about

This paper studies hypersurface exceptional singularities in [Formula: see text] defined by non-degenerate function. For each canonical hypersurface singularity, there exists a weighted homogeneous singularity such that the former is exceptional if and only if the latter is exceptional. So we study the weighted homogeneous case and prove that the number of weights of weighted homogeneous exceptional singularities are finite. Then we determine all exceptional singularities of the Brieskorn type of dimension 3.

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OpenAlex reports 26 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper studies hypersurface exceptional singularities in [Formula: see text] defined by non-degenerate function. For each canonical hypersurface singularity, there exists a weighted homogeneous singularity such that the former is exceptional if and only if the latter is exceptional. So we study the weighted homogeneous case and prove that the number of weights of weighted homogeneous exceptional singularities are finite. Then we determine all exceptional singularities of the Brieskorn type of dimension 3.

Key concepts: Hypersurface, Gravitational singularity, Mathematics, Homogeneous, Singularity, Dimension (graph theory), Pure mathematics, Degenerate energy levels

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