Read e-book online Algebraic Geometry and Commutative Algebra. In Honor of PDF

By Hiroaki Hijikata

ISBN-10: 0123480310

ISBN-13: 9780123480316

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Artin, Bull. Acad. , ser. Math. 22(1974) 1107-1109. D. Popescu: General Néron Desingularization, Nagoya Math. J. 100(1985) 97-126. C. Rotthaus: On the approximation property for excellent rings. Invent. Math. 88 (1987) 39-63. 44 Μ. ARTIN and C. SA. SA. Algebraic Geometry and Commutative Algebra in Honor of Masayoshi NAGATA pp. 45-58 (1987) On Rational Plane Sextics with Six Tritangents Wolf B A R T H * and Ross MOORE §0. I n t r o d u c t i o n . A rational plane sextic curve in general has ten nodes.

21, 1964. Α. Ploski: Note on a theorem of Μ. Artin, Bull. Acad. , ser. Math. 22(1974) 1107-1109. D. Popescu: General Néron Desingularization, Nagoya Math. J. 100(1985) 97-126. C. Rotthaus: On the approximation property for excellent rings. Invent. Math. 88 (1987) 39-63. 44 Μ. ARTIN and C. SA. SA. Algebraic Geometry and Commutative Algebra in Honor of Masayoshi NAGATA pp. 45-58 (1987) On Rational Plane Sextics with Six Tritangents Wolf B A R T H * and Ross MOORE §0. I n t r o d u c t i o n . A rational plane sextic curve in general has ten nodes.

D . Let p and q be prime ideals of C¿ such that p 2 and q D mCi + p. If p is a minimal prime ideal, we have dimC»q/pC¿q > 2 as dimCj/m^Ct < d — 1 and dimC¿/p = d -h 1. Κ p is not minimal, we put η = p Π A. Then C^ is Cohen-Macaulay as η is not a maximal ideal, whence C^pis Cohen-Macaulay. Therefore depth C»p+dun C¿q/pC¿q > 1-f 1 = 2. Hence there is an integer r > d such that m''F-^(Ci) = 0 for ¿ = 1 , . . , d by virture of [6]. Take an element y from m** such that height (J + yA) = d + 1, and put J = r ( r + 2/A).

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Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 1 by Hiroaki Hijikata


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