Oliver Labs Septic (deg 7)

 
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nextstep
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Posts: 538

PostPosted: Thu Sep 04, 2014 3:34 am    Post subject: Oliver Labs Septic (deg 7) Reply with quote

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 99-nodal 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 31-nodal quintic surface: The septic is seven-gon-symmetric 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": [
"Labs-Septic"
],
"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^6-3*7*x^4*y^2+5*7*x^2*y^4-7*y^6)+7*z*((x^2+y^2)^3-2^3*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": [
"Labs-Septic"
],
"Xmax": [
"5"
],
"Xmin": [
"-5"
],
"Ymax": [
"5"
],
"Ymin": [
"-5"
],
"Zmax": [
"5"
],
"Zmin": [
"-5"
]
}
}

LabsSeptic by taha_ab, on Flickr
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Cheers,
Abderrahman


Last edited by nextstep on Sat Oct 04, 2014 2:22 am; edited 1 time in total
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Fri Oct 03, 2014 10:34 am    Post subject: Reply with quote

hello next steps

you had missing a }in your formula.


cheer


denisc
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sat Oct 04, 2014 2:22 am    Post subject: Reply with quote

It's done ! thanks Cool
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Abderrahman
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