Breske Nonic (deg 9)

 
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sat Sep 06, 2014 2:57 am    Post subject: Breske Nonic (deg 9) Reply with quote

Hi all,
The maximum number of nodes on a surface of degree 9 (Nonic surface) is still unknown and the best construction is Chmutov's general one from 1992.
Breske's nonic surface is a variant of Chmutov's surface (an adaptation to have real singularities)
Breske found this variant of Chmutov's surface during the writing of her Diploma thesis (advisor D. van Straten) in 2005.
Code:
{
    "Iso3D": {
        "Cnd": [
            "(x^2+y^2+z^2)>9"
        ],
        "Component": [
            "Breske-Nonic"
        ],
        "Fxyz": [
            "(2*x^7-42*x^5*y^2+70*x^3*y^4-14*x*y^6-14*x^6+70*x^4*y^2+70*x^2*y^4-14*y^6+28*x^5+56*x^3*y^2+28*x*y^4-84*x^2*y^2+28*y^4-42*x^3-42*x*y^2+14*x^2-14*y^2+14*x) + 0.5* (64*z^7-112*z^5+56*z^3-7*z+5)"
        ],
        "Name": [
            "Breske-Nonic"
        ],
        "Xmax": [
            "3"
        ],
        "Xmin": [
            "-3"
        ],
        "Ymax": [
            "3"
        ],
        "Ymin": [
            "-3"
        ],
        "Zmax": [
            "3"
        ],
        "Zmin": [
            "-3"
        ]
    }
}


Breske-Nonic by taha_ab, on Flickr
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Abderrahman
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