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Monoid Hypersurfaces

In: Geometric Modeling and Algebraic Geometry

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pål Hermunn Johansen & Magnus Løberg & Ragni Piene, 2008. "Monoid Hypersurfaces," Springer Books, in: Bert Jüttler & Ragni Piene (ed.), Geometric Modeling and Algebraic Geometry, chapter 4, pages 55-77, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-72185-7_4
    DOI: 10.1007/978-3-540-72185-7_4
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