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MULTIPLICITY AND ŁOJASIEWICZ EXPONENT OF GENERIC LINEAR SECTIONS OF MONOMIAL IDEALS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 20 February 2015, pp. 191-201
- Print publication:
- April 2015
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- Article
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We 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.
