An Introduction to the Theory of Algebraic SurfacesThe purpose of these notes is to acquaint the reader with some basic facts of the theory of algebraic varieties. |
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affine representative affine varieties algebraic arithmetic genus assume birationally equivalent canonical divisor complete coordinate ring cycle on F D.Cm D₁ define degree q denote dim(V/k dimension effective cycle elements equation exists finite number fixed component follows homogeneous coordinates homogeneous prime ideal hypersurface integral closure intersection irreducible curve irreducible subvarieties kind with respect lemma linear system linearly maximal ideal minimal prime ideal module number of prime P₂ polar cycles polynomial prime cycle prime divisor prime divisorial cycles Proof Prop quotient field quotient ring regular at Q regular local ring residue field Seiten set of uniformizing subadjoint form subadjoint function subspace surface tangent theorem Tr dxdy transcendence basis uniformizing coordinates uniformizing parameters V₁ valuation vector space W₁ W₂ write X₁ y₁