Noether normalizations for local rings of algebraic varieties
HTML articles powered by AMS MathViewer
- by Kazuhiko Kurano PDF
- Proc. Amer. Math. Soc. 116 (1992), 905-910 Request permission
Abstract:
When $D$ is a regular subring of $A$ such that the inclusion map is finite, $D$ is called a Noether normalization of $A$. We will prove the existence of Noether normalizations of $A$, when $A$ is a local ring of a one-dimensional algebraic variety. Furthermore we will give a criterion for the existence and interesting examples.References
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Masayoshi Nagata, On rational surfaces. I. Irreducible curves of arithmetic genus $0$ or $1$, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 32 (1960), 351–370. MR 126443, DOI 10.1215/kjm/1250776405
- Michel Raynaud, Anneaux locaux henséliens, Lecture Notes in Mathematics, Vol. 169, Springer-Verlag, Berlin-New York, 1970 (French). MR 0277519
- Oscar Zariski, On Castelnuovo’s criterion of rationality $p_{a}=P_{2}=0$ of an algebraic surface, Illinois J. Math. 2 (1958), 303–315. MR 99990
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0120249
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 905-910
- MSC: Primary 13B22; Secondary 13H05, 14H20
- DOI: https://doi.org/10.1090/S0002-9939-1992-1100658-3
- MathSciNet review: 1100658