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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Johansen, P.H., Løberg, M., Piene, R. (2008). Monoid Hypersurfaces. In: Jüttler, B., Piene, R. (eds) Geometric Modeling and Algebraic Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72185-7_4
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DOI: https://doi.org/10.1007/978-3-540-72185-7_4
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