i1 : -- A general cubic fourfold of discriminant 26
X = specialCubicFourfold("Farkas-Verra C26",ZZ/33331);
o1 : ProjectiveVariety, cubic fourfold containing a surface of degree 7 and sectional genus 0
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i2 : describe X
o2 = Special cubic fourfold of discriminant 26
containing a 3-nodal surface of degree 7 and sectional genus 0
cut out by 13 hypersurfaces of degree 3
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i3 : time f = detectCongruence X;
S: surface of degree 7 and sectional genus 0 in PP^5 cut out by 13 hypersurfaces of degree 3
phi: cubic rational map from PP^5 to PP^12
Z=phi(P^5)
number lines contained in Z and passing through the point phi(p): 8
number 2-secant lines to S passing through p: 7
number 5-secant conics to S passing through p: 1
-- used 7.00581 seconds
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i4 : p := point ambient X -- random point on P^5
o4 = point of coordinates [-7901, -15944, -7086, 2968, 3085, 1]
o4 : ProjectiveVariety, a point in PP^5
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i5 : time C = f p; -- 5-secant conic to the surface
-- used 0.81582 seconds
o5 : ProjectiveVariety, curve in PP^5
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i6 : assert(dim C == 1 and degree C == 2 and dim(C * surface X) == 0 and degree(C * surface X) == 5 and isSubset(p, C))
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