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Defect and local uniformization

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Abstract

We give a simple algorithm showing that the reduction of the multiplicity of a characteristic \(p>0\) hypersurface singularity along a valuation is possible if there is a finite linear projection which is defectless. The method begins with the algorithm of Zariski to reduce multiplicity of hypersurface singularities in characteristic 0 along a valuation. This gives a simple demonstration that the only obstruction to local uniformization in positive characteristic is from defect arising in finite projections of singularities.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Steven Dale Cutkosky

  2. Equipe Géométrie et Dynamique, Institut Mathématique de Jussieu-Paris Rive Gauche, Université Paris 7, Bâtiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    Hussein Mourtada

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  1. Steven Dale Cutkosky
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  2. Hussein Mourtada
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Correspondence to Steven Dale Cutkosky.

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Dedicated to Professor Felipe Cano on the occasion of his 60th birthday.

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Steven Dale Cutkosky was partially supported by NSF. Hussein Mourtada was partially supported by a Miller Fellowship at the University of Missouri.

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Cutkosky, S.D., Mourtada, H. Defect and local uniformization. RACSAM 113, 4211–4226 (2019). https://doi.org/10.1007/s13398-019-00717-1

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