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Differential Geometry
Questions about algebraic curves and homogeneous polynomial equations
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[QUOTE="mathwonk, post: 6867390, member: 13785"] by the way, you may be interested in that specific curve, but geometers usually consider plane curves only up to isomorphism, and that conic I gave is linearly isomorphic to the much simpler one given by x^2 + y^2 + z^2 = 0, i.e. they are the same, after a linear change of coordinates. Up to linear isomorphism, there are only 3 different conics, given by x^2 (double line), x^2+y^2 (two distinct lines), and x^2+y^2+z^2 (smooth irreducible conic). this transformation of an arbitrary conic into such simpler ones is called "diagonalizing a quadratic form". (I assume here you are working over the complex numbers, as implied by your notation CP^2.) [/QUOTE]
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Questions about algebraic curves and homogeneous polynomial equations
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