The sequence of mixed Łojasiewicz exponents associated to pairs of monomial ideals

2020 ◽  
Vol 550 ◽  
pp. 108-141
Author(s):  
Carles Bivià-Ausina
Keyword(s):  
Monomial Ideals ◽  
Łojasiewicz Exponents

scholarly journals MULTIPLICITY AND ŁOJASIEWICZ EXPONENT OF GENERIC LINEAR SECTIONS OF MONOMIAL IDEALS

2015 ◽  
Vol 91 (2) ◽  
pp. 191-201 ◽  
Author(s):  
CARLES BIVIÀ-AUSINA
Keyword(s):  
Integral Closure ◽  
Monomial Ideals ◽  
Homogeneous Polynomials ◽  
Łojasiewicz Exponent ◽  
Łojasiewicz Exponents ◽  
Samuel Multiplicity ◽  
Linear Sections ◽  
Lojasiewicz Exponent

AbstractWe obtain a characterisation of the monomial ideals $I\subseteq \mathbb{C}[x_{1},\dots ,x_{n}]$ of finite colength that satisfy the condition $e(I)={\mathcal{L}}_{0}^{(1)}(I)\cdots {\mathcal{L}}_{0}^{(n)}(I)$, where ${\mathcal{L}}_{0}^{(1)}(I),\dots ,{\mathcal{L}}_{0}^{(n)}(I)$ is the sequence of mixed Łojasiewicz exponents of $I$ and $e(I)$ is the Samuel multiplicity of $I$. These are the monomial ideals whose integral closure admits a reduction generated by homogeneous polynomials.

scholarly journals A-graded methods for monomial ideals

2009 ◽  
Vol 322 (8) ◽  
pp. 2886-2904 ◽  
Author(s):  
Christine Berkesch ◽  
Laura Felicia Matusevich
Keyword(s):  
Monomial Ideals

Irreducible decomposition of monomial ideals

2005 ◽  
Vol 39 (3) ◽  
pp. 99-99 ◽  
Author(s):  
Shuhong Gao ◽  
Mingfu Zhu
Keyword(s):  
Monomial Ideals ◽  
Irreducible Decomposition

Unmixed Monomial Ideals of Dimension Two and Their Cohen–Macaulay Properties

2010 ◽  
Vol 38 (5) ◽  
pp. 1699-1714 ◽  
Author(s):  
Nguyen Cong Minh ◽  
Yukio Nakamura
Keyword(s):  
Monomial Ideals

scholarly journals Stanley’s conjecture for critical ideals

2011 ◽  
Vol 48 (2) ◽  
pp. 220-226
Author(s):  
Azeem Haider ◽  
Sardar Khan
Keyword(s):  
Polynomial Ring ◽  
Hilbert Function ◽  
Monomial Ideal ◽  
Monomial Ideals ◽  
Stanley Depth

Let S = K[x1,…,xn] be a polynomial ring in n variables over a field K. Stanley’s conjecture holds for the modules I and S/I, when I ⊂ S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non-critical monomial ideals we show the existence of a Stanley ideal with the same depth and Hilbert function.

scholarly journals A new index theorem for monomial ideals by resolutions

2018 ◽  
Vol 275 (3) ◽  
pp. 735-760
Author(s):  
Ronald G. Douglas ◽  
Mohammad Jabbari ◽  
Xiang Tang ◽  
Guoliang Yu
Keyword(s):  
Index Theorem ◽  
Monomial Ideals
Sign in / Sign up

Export Citation Format

Share Document