Zobrazeno 1 - 10
of 125
pro vyhledávání: '"Trung, Ngô Viêt"'
This paper studies the problem of which sequences of non-negative integers arise as the functions $\operatorname{reg} I^{n-1}/I^n$, $\operatorname{reg} R/I^n$, $\operatorname{reg} I^n$ for an ideal $I$ generated by forms of degree $d$ in a standard g
Externí odkaz:
http://arxiv.org/abs/2309.11631
By a classical result of Brodmann, the function $\operatorname{depth} R/I^t$ is asymptotically a constant, i.e. there is a number $s$ such that $\operatorname{depth} R/I^t = \operatorname{depth} R/I^s$ for $t > s$. One calls the smallest number $s$ w
Externí odkaz:
http://arxiv.org/abs/2308.15021
Let $I$ be the edge ideal of a connected non-bipartite graph and $R$ the base polynomial ring. Then $\operatorname{depth} R/I \ge 1$ and $\operatorname{depth} R/I^t = 0$ for $t \gg 1$. We give combinatorial conditions for $\operatorname{depth} R/I^t
Externí odkaz:
http://arxiv.org/abs/2212.14792
Autor:
Ha, Huy Tai, Trung, Ngo Viet
We survey recent studies and results on the following problem: which numerical functions can be the depth function of powers and symbolic powers of homogeneous ideals.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2106.08203
Autor:
Lam, Tran Thi Gia, Trung, Ngo Viet
Publikováno v:
Journal of Algebra 590 (2022), 313-337
Projective monomial curves correspond to rings generated by monomials of the same degree in two variables. Such rings always have finite Macaulayfication. We show how to characterize the Buchsbaumness and the Castelnuovo-Mumford regularity of these r
Externí odkaz:
http://arxiv.org/abs/2105.09190
Autor:
Quy, Pham Hung, Trung, Ngo Viet
Let $(R,\mathfrak m)$ be a local ring and $I, J$ two arbitrary ideals of $R$. Let $\operatorname{gr}_J(R/I)$ denote the associated ring of $R/I$ with respect to $J$, which corresponds to the normal cone in geometry. The main result of this paper show
Externí odkaz:
http://arxiv.org/abs/2012.14719
Publikováno v:
Math. Ann. 378 (2020), 951-969
We prove that two arbitrary ideals $I \subset J$ in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence. We also obtain a Principle of Specialization
Externí odkaz:
http://arxiv.org/abs/2008.00384
Autor:
Trung, Ngo Viet
Publikováno v:
Commutative algebra and combinatorics, Ramanujan Math. Soc. Lect. Notes 4, Ramanujan Math. Soc., 2007, 157-180
These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.
Comment: 23 pages, Lecture notes at the International Conference on Co
Comment: 23 pages, Lecture notes at the International Conference on Co
Externí odkaz:
http://arxiv.org/abs/1907.11427
Autor:
Nguyen, Hop Dang, Trung, Ngo Viet
Publikováno v:
Inventiones Mathematicae 218 (2019), 779-827
This paper addresses the problem of comparing minimal free resolutions of symbolic powers of an ideal. Our investigation is focused on the behavior of the function depth R/I^(t) = dim R - pd I^(t) - 1, where I^(t) denotes the t-th symbolic power of a
Externí odkaz:
http://arxiv.org/abs/1907.06468
Publikováno v:
Proc. Amer. Math. Soc. 149 (2021), 1837-1844
We settle a conjecture of Herzog and Hibi, which states that the function depth $S/Q^n$, $n \ge 1$, where $Q$ is a homogeneous ideal in a polynomial ring $S$, can be any convergent numerical function. We also give a positive answer to a long-standing
Externí odkaz:
http://arxiv.org/abs/1904.07587