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Mathematics
Differential Geometry
Questions about algebraic curves and homogeneous polynomial equations
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[QUOTE="Infrared, post: 6867080, member: 467682"] This defines a (finite) subset of ##\mathbb{C}P^1##, not ##\mathbb{C}P^2.## An algebraic curve in ##\mathbb{C}P^2## could be described as the zero set of a homogenous polynomial in ##3## variables. When you have a possibly nonhomoenous polynomial in ##n## variables, you can "homogenize" it by multiplying each term by an appropriate power of a new variable. For example, the equation ##x^2+y+1=0## defines a curve in the affine plane, but ##x^2+yz+z^2=0## defines a curve in the projective plane. These curves are related because if you take the points ##[x:y:z]## where ##z\neq 0## and identify it with the affine plane by scaling ##z## to be ##1##, then the two curves coincide. [/QUOTE]
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Forums
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Differential Geometry
Questions about algebraic curves and homogeneous polynomial equations
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