Derivations preserving a monomial ideal

Tadesse, Yohannes

doi:10.1090/S0002-9939-09-09922-5

Derivations preserving a monomial ideal
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by Yohannes Tadesse PDF

Proc. Amer. Math. Soc. 137 (2009), 2935-2942 Request permission

Abstract:

Let $I$ be a monomial ideal in a polynomial ring $\mathbf {A}=\mathbf {k}[x_1,\ldots , x_n]$ over a field $\mathbf {k}$ of characteristic 0, $T_{\mathbf {A}/\mathbf {k}} (I)$ be the module of $I$-preserving $\mathbf {k}$-derivations on $\mathbf {A}$ and $G$ be the $n$-dimensional algebraic torus on $\mathbf {k}$. We compute the weight spaces of $T_{\mathbf {A}/\mathbf {k}} (I)$ considered as a representation of $G$. Using this, we show that $T_{\mathbf {A}/\mathbf {k}} (I)$ preserves the integral closure of $I$ and the multiplier ideals of $I$.

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