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Advanced Algebraic Curves problem

  1. Dec 5, 2009 #1
    [Question]
    Let p1, p2 and p3 be 3 distinct points in PC2( Projective space, ie
    (z0,z1,z2) belong to PC2) Find the dimension of the linear system of
    cubics containing these 3 points.


    I have solved it for the non collinear case, by taking a projective
    transformation of the 3 points to [1,0,0],[0,1,0] and [0,0,1]
    respectively.
    And substituting those values into the equation of a cubic, to get
    that there are 6 coefficients remaining, therefore the dimension of
    the linear system is 6 by definition.

    But I am stuck on the collinear case (or maybe it can be shown generally?), thanks in advance for any help
    that can be given.
     
  2. jcsd
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