By Hiroaki Hikikata

ISBN-10: 0123480329

ISBN-13: 9780123480323

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Extra resources for Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 2

Example text

With notation as above, we have A7(y) C A'7(y) = ( J m 67 A'[m}(y) for any 7 € Γ ( η ) . Proof. The first inclusion is obvious by definition. So, we show the second B^ a reduced P-homomorphism, we equality. , tm} might be empty (cf. 1)). Then, for any Q C m such that Q — Q Π Β with Q G Ass(Cyk/yCyk), the following diagram: Clk — • 5 ^ ® β . 8, there exists Q G Ass(Cmh/yCmh) 463 for some h G A 7fc m such that Q = QnC 7fc. 8. Q = Q Π Cjk G Ass(C7k/yCyk) whenever h G A 7 . f c m Notation being as above, let B # be the (J,b)-adic completion # of Β and c* = Πς#€6Ρ(β#) ^ = q f n---n q^.

To appear in J. Math. Kyoto Univ. [13] P. Wagreich: Elliptic singularities of surfaces. Amer. J. , 92(1970), 419-454. 452 K. NlSHIGUCHI Kenji NlSHIGUCHI Department of Mathematics Faculty of Science Osaka University Toyonaka, Osaka, 560 Japan Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Ν A G A T A pp. 453-467 (1987) Ideal-adic Completion of Noetherian Rings I I Jun-ichi N l S H l M U R A and Toshio NISHIMURA Introduction. This paper is the sequel to our previous note [16]. Here again we study Lifting Problem on ideal-adically complete noetherian rings.

This is a contradiction. d. 1) continued. Take λ : Υ' —• Y so that degA is as small as possible. 10], λ is étale outside of the closed subset Ζ of Y with codimy Ζ > 2. 1). d. References [Κ] Y . Kawamata, Minimal models and the Kodaira dimension of algebraic fiber spaces, J. für die reine und angew. Math. 363 (1985), 1-46. [V] E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fiber spaces, in Algebraic and Analytic Varieties, (S. ), Advanced Studies in Pure Math.

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Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 2 by Hiroaki Hikikata

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