On the reduction number of some graded algebras

Bresinsky, Henrik; Hoa, Lê

doi:10.1090/S0002-9939-99-04622-5

On the reduction number of some graded algebras
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by Henrik Bresinsky and Lê Tuân Hoa PDF

Proc. Amer. Math. Soc. 127 (1999), 1257-1263 Request permission

Abstract:

The main result of the paper confirms, for generic coordinates, a conjecture which states that $r(R/I) \le r(R/in(I))$. Here $I$ is a homogeneous polynomial ideal in $R$ and $r(R/I)$ and $r(R/in(I))$ are the reduction numbers.

References

Henrik Bresinsky, Minimal free resolutions of monomial curves in $\textbf {P}^{3}_{k}$, Linear Algebra Appl. 59 (1984), 121–129. MR 743050, DOI 10.1016/0024-3795(84)90163-0
H. Bresinsky, F. Curtis, M. Fiorentini, and L. T. Hoa, On the structure of local cohomology modules for monomial curves in $\textbf {P}^3_K$, Nagoya Math. J. 136 (1994), 81–114. MR 1309382, DOI 10.1017/S0027763000024971
David Bayer and Michael Stillman, A criterion for detecting $m$-regularity, Invent. Math. 87 (1987), no. 1, 1–11. MR 862710, DOI 10.1007/BF01389151
Eisenbud, D.: Commutative Algebra with a view towards Algebraic geometry. Springer-Verlag, Berlin-Heidelberg-New York, 1995.
Hans-Gert Gräbe, Homology modules and standard bases, Beiträge Algebra Geom. 32 (1991), 11–20. MR 1140761
Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
Trung, N. V.: Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc. 102(1987), 229-236
Vasconcelos V. W.: The degrees of graded modules, In: Proceedings of Summer School on Commutative Algebra, Bellaterra 1996, Vol. II, CRM Publication, 141-196.