Wild hypersurfaces
Andrew Crabbe, Graham J. Leuschke
TL;DR
This paper investigates the classification of hypersurfaces with high multiplicity and dimension, revealing that such conditions lead to complex, 'wild' Cohen-Macaulay representation types.
Contribution
It establishes a criterion linking high multiplicity and dimension to the wild Cohen-Macaulay type of hypersurfaces.
Findings
Hypersurfaces of dimension ≥2 and multiplicity ≥4 are of wild Cohen-Macaulay type.
The result extends understanding of the complexity of hypersurface singularities.
Provides a classification boundary for Cohen-Macaulay representation types.
Abstract
Complete hypersurfaces of dimension at least 2 and multiplicity at least 4 have wild Cohen-Macaulay type.
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Taxonomy
TopicsComputational Geometry and Mesh Generation