Cohomological dimension, Lyubeznik numbers, and connectedness in mixed characteristic
نویسندگان
چکیده
منابع مشابه
Cohomological Dimension, Connectedness Properties and Initial Ideals
In this paper we will compare the connectivity dimension c(P/I) of an ideal I in a polynomial ring P with that of any initial ideal of I. Generalizing a theorem of Kalkbrener and Sturmfels [18], we prove that c(P/LT≺(I)) ≥ min{c(P/I), dim(P/I)−1} for each monomial order ≺. As a corollary we have that every initial complex of a Cohen-Macaulay ideal is strongly connected. Our approach is based on...
متن کاملGröbner Deformations, Connectedness and Cohomological Dimension
In this paper we will compare the connectivity dimension c(P/I) of an ideal I in a polynomial ring P with that of any initial ideal of I. Generalizing a theorem of Kalkbrener and Sturmfels [18], we prove that c(P/LT≺(I)) ≥ min{c(P/I), dim(P/I)−1} for each monomial order ≺. As a corollary we have that every initial complex of a Cohen-Macaulay ideal is strongly connected. Our approach is based on...
متن کاملLyubeznik Numbers of Monomial Ideals
Let R = k[x1, ..., xn] be the polynomial ring in n independent variables, where k is a field. In this work we will study Bass numbers of local cohomology modules H I (R) supported on a squarefree monomial ideal I ⊆ R. Among them we are mainly interested in Lyubeznik numbers. We build a dictionary between the modules H I (R) and the minimal free resolution of the Alexander dual ideal I∨ that all...
متن کاملOn Lyubeznik Numbers of Projective Schemes
Let X be an arbitrary projective scheme over a field k. Let A be the local ring at the vertex of the affine cone for some embedding ι : X →֒ P n k . G. Lyubeznik asked (in [15]) whether the integers λi,j(A) (defined in [14]), called the Lyubeznik numbers of A, depend only on X, but not on the embedding. In this paper, we make a big step toward a positive answer to this question by proving that i...
متن کاملCohomological Dimension of Markov Compacta
We rephrase Gromov’s definition of Markov compacta, introduce a subclass of Markov compacta defined by one building block and study cohomological dimensions of these compacta. We show that for a Markov compactum X, dimZ(p) X = dimQ X for all but finitely many primes p where Z(p) is the localization of Z at p. We construct Markov compacta of arbitrarily large dimension having dimQ X = 1 as well ...
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: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.07.019