Monoid Hypersurfaces

Pål Hermunn Johansen (), Magnus Løberg () and Ragni Piene ()
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Pål Hermunn Johansen: University of Oslo, Centre of Mathematics for Applications and Department of Mathematics
Magnus Løberg: University of Oslo, Centre of Mathematics for Applications and Department of Mathematics
Ragni Piene: University of Oslo, Centre of Mathematics for Applications and Department of Mathematics

Chapter 4 in Geometric Modeling and Algebraic Geometry, 2008, pp 55-77 from Springer

Abstract: 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.

Date: 2008
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DOI: 10.1007/978-3-540-72185-7_4

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