Elements of Algebraic GeometryCourant Institute of Mathematical Sciences, New York University, 1955 - Geometry, Algebraic - 142 pages |
Contents
Valuation Rings Places and Valuations | 32 |
Absolutely Irreducible Varieties | 63 |
Projective Varieties | 104 |
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Common terms and phrases
a₁ absolutely irreducible alge algebraic geometry algebraic points algebraically closed algebraically free algebraically independent assume automorphism belong called closure coefficients common non-trivial solution component varieties consequently consists containing d₁ degree of transcendency denote determined dimension domain equation exists extension F and k¹/p F are linearly F is separably f₁ field of definition finite number form of degree form of positive Hence homogeneous algebraic set homogeneous varieties homomorphism ideal of k[X implies integrally closed intersection isomorphism k¹/p are linearly kernel largest defining ideal lemma Let f let us show linear linearly disjoint linearly independent local ring maximal ideal monomials non-units non-zero obtain ordered group polynomial positive degree prime ideal projective varieties Proof prove quotient field resultant satisfied specialization subset subvariety suppose Theorem 3.1 transcendence base trivial valuation ring variables well-defined whence wish to show x₁ zero ед