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Some remarks concerning Demazure’s construction of normal graded rings

Published online by Cambridge University Press:  22 January 2016

Keiichi Watanabe
Keiichi Watanabe*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University Fukazawa, Setagaya-ku Tokyo, 158 Japan
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In [1], Demazure showed a new way of constructing normal graded rings using the concept of “rational coefficient Weil divisors” of normal projective varieties and he showed, among other things, the following

THEOREM ([1], 3.5). If R = ⊕n ≥ 0Rn is a normal graded ring of finite type over a field k and if T is a homogeneous element of degree 1 in the quotient field of R, then there exists unique divisor D ∈ Div (X, Q) (X = Proj (R)), such that for every n ≧ 0.(See (1.1) for the definition of

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 83 , October 1981 , pp. 203 - 211
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[1] Demazure, M., Anneaux gradues normaux, in Séminaire Demazure-Giraud-Teissier, Singularités des surfaces, Ecole Polytechnique, 1979.Google Scholar
[2] Goto, S. and Watanabe, K., On graded rings, I. J. Math. Soc. Japan, 30 (1978), 179–213.Google Scholar
[3] Hochster, M. and Roberts, J. L., Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. in Math., 13 (1974), 115–175.Google Scholar
[4] Kempf, G., Knudsen, F., Mumford, D. and Saint-Donat, B., Toroidal embeddings, I. Lecture Notes in Math. 339, Springer, 1973.CrossRefGoogle Scholar
[5] Mori, S., Graded factorial domains, Japan. J. Math., 3 (1977), 223–238.Google Scholar
[6] Pinkham, H., Normal surface singularities with C*-action, Math. Ann., 227 (1977), 183–193.Google Scholar
[7] Samuel, P., Lectures on Unique Factorization Domains, Tata Inst. Fund. Res., Bombay, 1964.Google Scholar
[8] Altman, A. and Kleiman, S., Introduction to Grothendieck Duality Theory, Lecture Notes in Math., 146, Springer, 1970.CrossRefGoogle Scholar