nextstep Site Admin
Joined: 06 Jan 2007 Posts: 538

Posted: Thu Sep 04, 2014 3:34 am Post subject: Oliver Labs Septic (deg 7) 


Hi all,
In 2004, Oliver Labs constructed the first surface of odd degree greater than five which exceeded Chmutov's general lower bound for μ(d) (99 ≤ µ(7) ≤ 104)
The geometry of Labs's 99nodal septic (which he constructed during the writing of his Ph.D. thesis,with advisor van Straten) is very similar to Barth's construction of the 31nodal quintic surface: The septic is sevengonsymmetric and the symmetry plane y=0 cuts the septic in a curve which factors into a line and a nodal sextic curve.
99 ordinary double points is the maximum number known for any septic surface.
Quote:  {
"Iso3D": {
"Cnd": [
"(x^2+y^2+z^2)>25"
],
"Component": [
"LabsSeptic"
],
"Const": [
" w = 1.0",
"a1 = (12/7)*(0.14010685)^2 (384/49)*(0.14010685) (8/7)",
"a2 = (32/7)*(0.14010685)^2 +(24/49)*(0.14010685) 4",
"a3 = 4*(0.14010685)^2 +(24/49)*(0.14010685) 4",
"a4 = (8/7)*(0.14010685)^2 +(8/49)*(0.14010685) 8/7",
"a5 = 49*(0.14010685)^2 7*(0.14010685) +50"
],
"Fxyz": [
"(x*(x^63*7*x^4*y^2+5*7*x^2*y^47*y^6)+7*z*((x^2+y^2)^32^3*z^2*(x^2+y^2)^2+2^4*z^4*(x^2+y^2))2^6*z^7)((z+a5*w)*((z+w)*(x^2+y^2)+a1*z^3+a2*z^2*w+a3*z*w^2+a4*w^3)^2)"
],
"Name": [
"LabsSeptic"
],
"Xmax": [
"5"
],
"Xmin": [
"5"
],
"Ymax": [
"5"
],
"Ymin": [
"5"
],
"Zmax": [
"5"
],
"Zmin": [
"5"
]
}
} 
LabsSeptic by taha_ab, on Flickr _________________ Cheers,
Abderrahman
Last edited by nextstep on Sat Oct 04, 2014 2:22 am; edited 1 time in total 
