Monoid hypersurfaces

Details Monoid hypersurfaces Monoid hypersurfaces

2006-12-20

arxiv.org/abs/math/0612582v1

Mathematics

Algebraic Geometry

22 pages, 4 figures

Scientific paper

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d-1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design. We study properties of monoids in general and of monoid surfaces in particular. The main results include a description of the possible real forms of the singularities on a monoid surface other than the (d-1)-uple point. These results are applied to the classification of singularities on quartic monoid surfaces, complementing earlier work on the subject.

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