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...A algebraic geometry contents i ane varieties projective morphisms rational maps nonsingular curves intersections in space supplement representing families lines p ii sheaves schemes first properties of separated and proper modules divisors the following are notes from course taught by robin hartshorne intending to cover rst two chapters his text only supplementary comments examples included affine example if k r then variety z y mx b denes line note that x gives circle but consists single point this is because c q or f think as contained closure do look for points over its usual topology has dimr since irreducible subset choose so hx local we dene m gr where residue eld have dim...