Hilbert-Kunz density function and Hilbert-Kunz multiplicity
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 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 کاملHilbert-kunz Multiplicity and Reduction Mod P
In this paper, we study the behaviour of Hilbert-Kunz multiplicities (abbreviated henceforth to HK multiplicities) of the reductions to positive characteristics of an irreducible projective curve in characteristic 0. For instance, consider the following question. Let f be a nonzero irreducible homogeneous element in the polynomial ring Z[X1, X2, . . . , Xr], and for any prime number p ∈ Z, let ...
متن کاملSome Extensions of Hilbert-kunz Multiplicity
Let R be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do not assume that their quotient has finite length. In this paper, we develop various sufficient numerical criteria for when the tight closures of these ideals (or submodules) match. For some of the criteria we ...
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 کاملذخیره 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: Transactions of the American Mathematical Society
سال: 2018
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7268