Transcription of Introductory Geometry: Algebraic Geometry
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Introductory Geometry: Algebraic Geometry
Introductory GeometryCourse No. 100 351 Fall 2005 Second Part: Algebraic GeometryMichael StollContents1. What Is Algebraic Geometry ?22. Affine Spaces and Algebraic Sets33. Projective Spaces and Algebraic Sets64. Projective Closure and Affine Patches95. Morphisms and Rational Maps116. Curves Local Properties147. B ezout s Is Algebraic Geometry ?Linear Algebracan be seen (in parts at least) as the study of systems of linearequations. In geometric terms, this can be interpreted as the study of linear (oraffine) subspaces ofCn(say).
3 denominators. For the unit circle we obtain x2 + y2 = z2; a general line in P2 is given by ax+by+cz= 0 with a,b,cnot all zero. (The line at infinity has equation z= 0, for example.)
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