Multiplicities and Reduction Numbers
نویسنده
چکیده
Let (R,m) be a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.
منابع مشابه
Generalized Kneser Coloring Theorems with Combinatorial Proofs (Erratum)
In [5], we presented a lower bound for the chromatic numbers of hypergraphs KG sS, “generalized r-uniform Kneser hypergraphs with intersection multiplicities s.” It generalized previous lower bounds by Kř́ıž [1, 2] for the case s = (1, . . . , 1) without intersection multiplicities, and by Sarkaria [4] for S = ([n] k ) . The following two problems that arise for intersection multiplicities si > ...
متن کاملMultiplicities of Integer Arrays
We prove a general theorem about the multiplicity of the entries in certain integer arrays which is best possible in general. As an application we give non-trivial bounds for the multiplicities of several well-known combinatorial arrays including the binomial coefficients, Narayana numbers and the Eulerian numbers. For the binomial coefficients we obtain the result of Singmaster.
متن کاملHilbert Functions of Multigraded Algebras, Mixed Multiplicities of Ideals and Their Applications
This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicities of blowup algebras and mixed volumes of polytopes.
متن کاملMulti-graded Hilbert functions, mixed multiplicities
Multiplicities of ideals are useful invariants, which in good rings determine the ideal up to integral closure. Mixed multiplicities are a collection of invariants of several ideals, generalizing multiplicities, and capturing some information on the interactions among ideals. Teissier and Risler [Tei73] were the first to develop mixed multiplicities, in connection with Milnor numbers of isolate...
متن کاملOn generalized Kneser hypergraph colorings
In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KG sS, “generalized r-uniform Kneser hypergraphs with intersection multiplicities s.” It generalized previous lower bounds by Kř́ıž (1992/2000) for the case s = (1, . . . , 1) without intersection multiplicities, and by Sarkaria (1990) for S = ([n] k ) . Here we discuss subtleties and difficulti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007