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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
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