named by Hauser. Its singular points form the line. The defining polynomial is an irreducible
polynomial, although its real image has upper and lower portions with different
local shapes. For fixed ,
its section near
has a cusp opening into .
The substitution
gives
Removing the factor
gives the equation of the calypso surface. This
substitution is a chart of an algebraic blow-up,
illustrating how a change of variables can simplify singularities
(Hauser 2007, p. 33).
Hauser, H. "Desingularization of Ideals and Varieties." In Singularity Theory: Proceedings of the 2005 Marseille Singularity School and
Conference (Ed. D. Chéniot, N. Dutertre, C. Murolo, D. Trotman,
and A. Pichon). Singapore: World Scientific, pp. 33-69, 2007. https://doi.org/10.1142/9789812707499_0002.Hauser,
H. "Gallery of Singular Algebraic Surfaces: Calyx." https://homepage.univie.ac.at/herwig.hauser/gallery.html.
. The defining polynomial is an irreducible
polynomial, although its real image has upper and lower portions with different
local shapes. For fixed 
,
its section near 
has a cusp opening into 
.
gives
gives the equation of the calypso surface. This
substitution is a chart of an algebraic blow-up,
illustrating how a change of variables can simplify singularities
(Hauser 2007, p. 33).
