On local cohomology and Hilbert function of powers of ideals

2003 ◽  
Vol 112 (1) ◽  
pp. 77-92 ◽  
Author(s):  
L� Tu�n Hoa ◽  
Eero Hyry
Keyword(s):  
Hilbert Function ◽  
Local Cohomology ◽  
Powers Of Ideals

scholarly journals Length of local cohomology of powers of ideals

2018 ◽  
Vol 371 (5) ◽  
pp. 3483-3503 ◽  
Author(s):  
Hailong Dao ◽  
Jonathan Montaño
Keyword(s):  
Local Cohomology ◽  
Powers Of Ideals

scholarly journals Tight closure of powers of ideals and tight hilbert polynomials

2019 ◽  
Vol 169 (2) ◽  
pp. 335-355
Author(s):  
KRITI GOEL ◽  
J. K. VERMA ◽  
VIVEK MUKUNDAN
Keyword(s):  
Local Ring ◽  
Hilbert Function ◽  
Simplicial Complexes ◽  
Primary Ideal ◽  
Hilbert Polynomial ◽  
Prime Characteristic ◽  
Tight Closure ◽  
Powers Of Ideals ◽  
Hilbert Polynomials

AbstractLet (R, ) be an analytically unramified local ring of positive prime characteristic p. For an ideal I, let I* denote its tight closure. We introduce the tight Hilbert function $$H_I^*\left( n \right) = \Im \left( {R/\left( {{I^n}} \right)*} \right)$$ and the corresponding tight Hilbert polynomial $$P_I^*\left( n \right)$$, where I is an m-primary ideal. It is proved that F-rationality can be detected by the vanishing of the first coefficient of $$P_I^*\left( n \right)$$. We find the tight Hilbert polynomial of certain parameter ideals in hypersurface rings and Stanley-Reisner rings of simplicial complexes.

Hilbert function of powers of ideals of low codimension

1999 ◽  
Vol 230 (4) ◽  
pp. 753-784 ◽  
Author(s):  
A. Conca ◽  
G. Valla
Keyword(s):  
Hilbert Function ◽  
Powers Of Ideals

scholarly journals Limit behavior of the rational powers of monomial ideals

2021 ◽  
Author(s):  
James Lewis
Keyword(s):  
Local Cohomology ◽  
Integral Closure ◽  
Monomial Ideals ◽  
Limit Behavior ◽  
Associated Primes ◽  
Powers Of Ideals ◽  
Symbolic Powers ◽  
Local Cohomology Modules ◽  
Cohomology Modules

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

scholarly journals Artinianness of local cohomology modules

2014 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Moharram Aghapournahr ◽  
Leif Melkersson
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Cohomology Modules

On the associated primes of local cohomology modules

1999 ◽  
Vol 27 (12) ◽  
pp. 6191-6198 ◽  
Author(s):  
K. Khashyarmanesh ◽  
Sh Salarian
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules
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