is surjective, i.e., hypersurfaces of degree k cut out a complete linear system on X . We say that X is k–regular if H(P, IX(k − i)) = 0 for all i ≥ 1, where IX is the sheaf of ideals of X in OPr . It is easy to see that X is (k + 1)– regular if and only if X is k–normal and H(X,OX(k − i)) = 0 for all i > 0. Let reg(X) = min{k ∈ Z : X is k–regular}. The importance of k–regularity stems from the...

Let A be a noetherian AS regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and grA the category of finitely generated graded left A-modules. Following Jørgensen, we define the CastelnuovoMumford regularity reg(M•) of a complex M• ∈ D(grA) in terms of the local cohomologies or the minimal projective resolution of M•. Let A be the quadratic dual ring of A. ...

We investigate the asymptotic behaviour of Castelnuovo-Mumford regularity Ext and Tor, with respect to homological degree, over complete intersection rings. derive from a theorem Gulliksen linearity result for modules in high degrees. show similar under additional hypothesis that enough Tor are supported dimension at most one; we then provide examples showing could be pretty hectic when latter ...

let $l$ be a lattice in $zz^n$ of dimension $m$. we prove that there exist integer constants $d$ and $m$ which are basis-independent such that the total degree of any graver element of $l$ is not greater than $m(n-m+1)md$. the case $m=1$ occurs precisely when $l$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. as a corollary, we show t...

This paper shows that Bitcoin is not correlated to a general uncertainty index as measured by the Google Trends data of Castelnuovo and Tran (2017). Instead, linked attention measure specific for cryptocurrency market. First, we find bidirectional relationship between returns up six days. Second, information flows from volatility seem be larger than in other direction. These relations hold acro...

For a partition λ of n ∈ N , let I Sp be the ideal R = K [ x 1 … ] generated by all Specht polynomials shape . In previous paper, second author showed that if / is Cohen-Macaulay, then either ( − d ) or and converse true char 0 this we compute Hilbert series for Hence, get Castelnuovo-Mumford regularity when it Cohen-Macaulay. particular, has + 2 -linear resolution in Cohen–Macaulay case.

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. In this paper, we obtain upper bounds for Castelnuovo-Mumford regularity of I(G)q in terms certain combinatorial invariants associated with G. We also prove weaker version conjecture by Alilooee, Banerjee, Beyarslan Hà on an bound conjectured class vertex decomposable graphs. Using these results, explicitly compute sev...

We investigate the rational powers of ideals. find that in case monomial ideals, canonical indexing leads to a characterization yielding symbolic squarefree ideals are indeed themselves. Using connection with techniques, we use splittings show convergence depths and normalized Castelnuovo–Mumford regularities. Stanley for powers, as consequence this, before-now unknown integral closure powers. ...