Notes on Algebraic Geometry |
Common terms and phrases
algebraic geometry algebraic points algebraically closed field assume centre closure contains Corollary define definition degree dimension divisor of poles entire function equation equivalent exists an element f₁(X field of constants finite number fixed places formal power series function field genus ground field H¹(V homogeneous hypersurface implies inequivalent integral closure integrally closed intersection multiplicity irreducible affine irreducible k-variety irreducible projective curve isomorphism k-isomorphism L(D+P L(ME Lemma linear series linearly independent local ring mapping maximal ideal non-trivial place non-units non-zero element P₁ parallelotope plane curve polynomial positive divisor prime ideal projective variety proof of Theorem Proposition 9 prove real numbers repartition representative cone Riemann-Roch Theorem separable extension shows singular point subfield subring subspace uniformizing parameter unique universal domain V₁ valuation ring value group vanishes vector space vp(t Vp(x Weil-differential zero χε