Seepferdchen

silviana amethyst

Equation ¶

Properties: ¶

• degree 6
• one single singular point at the origin, smooth otherwise
• unbounded

Some story ¶

Seepferdchen was very challending to print. The equation in every source I used was incorrect. I only obtained the correct equation after emailing Herwig Hauser (he responded almost immediately!) and then doing some guess and check.

I made five copies of this surface to give as the Early Career prize for the SIAM Activity Group on Applied Algebraic Geometry. It’s given every two years. The first went to Pierre Lariez.

This was the first surface I emblazoned with its name and equation. It makes the object more difficult to print, but it’s totally worth it. Long term goal: do this for every surface in the gallery.

Bertini_real input files ¶

input

% this input file contains the corrected equation for the `seepferdchen` or `seahorse` surface, used so many places, but always with incorrect equation...
% the incorrect given equation is
% (x^2-y^3)^2-(x+y^2)*z^3=0
% as given
% http://homepage.univie.ac.at/herwig.hauser/gallery.html
% and so many other places.
CONFIG
randomseed: 1;
SHARPENDIGITS: 20;
tracktype: 1;
condnumthreshold: 1e300;
mptype: 2;
tracktolbeforeeg: 1e-7;
tracktolbeforeeg: 1e-9;
finaltol: 1e-13;
securitylevel: 1;
maxstepsize: 0.05;
ODEPREDICTOR: 7;
ENDGAMENUM: 2;
numsamplepoints: 6;
maxnewtonsteps: 0;
maxstepsbeforenewton: 1;
END;
INPUT

variable_group x, y, z;
function f1;
f1 = x^4-2.5*x^2*y^3 -x*z^3 +y^6 -y^2*z^3;
END;