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nextstep

Joined: 06 Jan 2007
Posts: 539

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 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
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Fri Oct 03, 2014 10:34 am    Post subject: hello next steps you had missing a }in your formula. cheer denisc
nextstep

Joined: 06 Jan 2007
Posts: 539

 Posted: Sat Oct 04, 2014 2:22 am    Post subject: It's done ! thanks _________________Cheers, Abderrahman
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