On the Hilbert-Kunz Function and Koszul Homology
نویسندگان
چکیده
منابع مشابه
Hilbert - Kunz Multiplicity
1. An estimate for the HK multiplicity of a curve Let X be a nonsingular projective curve over an algebraically closed field k of characteristic p > 0. We fix the following notations for a vector bundle V on X . If 0 = F0 ⊂ F1 ⊂ F2 ⊂ · · · ⊂ Ft ⊂ Ft+1 = V is the Harder-Narasimhan filtration (or HN filtration) then we denote μ(Fi) = μ(Fi/Fi−1) and μ(Fi) = μ(Fi+1/Fi). Now throughout the section w...
متن کاملThe Hilbert-kunz Function in Graded Dimension Two
Suppose that (R,m) is a local Noetherian or a standard-graded ring of dimension d containing a field K of positive characteristic p. Let I denote an m-primary ideal and set I [q] = (f q : f ∈ I), q = p. The function e 7→ λ(R/I [p e]), where λ denotes the length, is called the Hilbert-Kunz function of the ideal I and was first considered by Kunz in [9]. Monsky showed in [12] that this function h...
متن کامل2 Minimal Hilbert - Kunz Multiplicity
In this paper, we ask the following question: what is the minimal value of the difference e HK (I) − e HK (I ′) for ideals I ′ ⊇ I with l A (I ′ /I) = 1? In order to answer to this question, we define the notion of minimal Hilbert-Kunz multiplicity for strongly F-regular rings. Moreover, we calculate this invariant for quotient singularities and for the coordinate ring of the Segre embedding: P...
متن کاملOn Rings with Small Hilbert{kunz Multiplicity
A result of Watanabe and Yoshida says that an unmixed local ring of positive characteristic is regular if and only if its Hilbert-Kunz multiplicity is one. We show that, for fixed p and d, there exist a number ǫ(d, p) > 0 such that any nonregular unmixed ring R its Hilbert-Kunz multiplicity is at least 1+ ǫ(d, p). We also show that local rings with sufficiently small Hilbert-Kunz multiplicity a...
متن کاملcompactifications and function spaces on weighted semigruops
chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1995
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1212