CongruenceOfCurves EmbeddedProjectiveVariety -- get the curve of a congruence passing through a point

Synopsis

• Operator: SPACE

• Usage:

  f(p)

• Inputs:
  • f, a congruence of curves, a congruence of curves to a surface inside a variety $Y$
  • p, an embedded projective variety, a general point on $Y$ (that is, a point on $Y$ outside a certain proper Zariski closed subset)
• Outputs:
  • an embedded projective variety, the unique curve of the congruence $f$ that passes through $p$

Description

i1 : X = specialCubicFourfold surface {3,4};

o1 : ProjectiveVariety, cubic fourfold containing a surface of degree 5 and sectional genus 1

i2 : f = detectCongruence(X,1);

o2 : Congruence of 2-secant lines to surface in PP^5

i3 : C = f point ambient X;

o3 : ProjectiveVariety, curve in PP^5

i4 : member(C,f)

o4 = true

i5 : assert oo

See also

• detectCongruence -- detect and return a congruence of secant curves to a surface
• isMember(EmbeddedProjectiveVariety,CongruenceOfCurves) -- test membership in a congruence of curves