Local singularities such that all deformations are tangentially flat

Herzog, Bernd

doi:10.1090/S0002-9947-1991-0986026-7

Local singularities such that all deformations are tangentially flat
HTML articles powered by AMS MathViewer

by Bernd Herzog

Trans. Amer. Math. Soc. 324 (1991), 555-601

DOI: https://doi.org/10.1090/S0002-9947-1991-0986026-7

PDF | Request permission

Abstract:

We give a criterion for a local ring $({B_0},{\mathfrak {n}_0})$ containing a field to have only tangentially flat deformations. Various examples of such local rings are constructed.

References

Algèbre commutative

Corrado De Concini, David Eisenbud, and Claudio Procesi, Hodge algebras, Astérisque, vol. 91, Société Mathématique de France, Paris, 1982. With a French summary. MR 680936

Eléments de géométrie algébrique

Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
B. Herzog, Die Wirkung lokaler Homomorphismen auf die Hilbertfunktion, Math. Nachr. 97 (1980), 103–115 (German). MR 600827, DOI 10.1002/mana.19800970110
B. Herzog, On a relation between the Hilbert functions belonging to a local homomorphism, J. London Math. Soc. (2) 25 (1982), no. 3, 458–466. MR 657502, DOI 10.1112/jlms/s2-25.3.458
Bernd Herzog, A criterion for tangential flatness, Manuscripta Math. 43 (1983), no. 2-3, 219–228. MR 707045, DOI 10.1007/BF01165831
J. Herzog, Strict local rings, Proc. Amer. Math. Soc. 84 (1982), no. 2, 165–172. MR 637161, DOI 10.1090/S0002-9939-1982-0637161-4
Heisuke Hironaka, Certain numerical characters of singularities, J. Math. Kyoto Univ. 10 (1970), 151–187. MR 292831, DOI 10.1215/kjm/1250523817
Anthony Iarrobino, Compressed algebras: Artin algebras having given socle degrees and maximal length, Trans. Amer. Math. Soc. 285 (1984), no. 1, 337–378. MR 748843, DOI 10.1090/S0002-9947-1984-0748843-4
Christer Lech, Inequalities related to certain couples of local rings, Acta Math. 112 (1964), 69–89. MR 161876, DOI 10.1007/BF02391765
Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
Peter Schenzel, Über die freien Auflösungen extremaler Cohen-Macaulay-Ringe, J. Algebra 64 (1980), no. 1, 93–101 (German). MR 575785, DOI 10.1016/0021-8693(80)90136-2