Ordinary and symbolic powers are Golod

Jürgen Herzog; Craig Huneke

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arXiv · 1212.6579

Ordinary and symbolic powers are Golod

Jürgen Herzog·Craig Huneke

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Abstract

Let $S$ be a positively graded polynomial ring over a field of characteristic 0, and $I\subset S$ a proper graded ideal. In this note it is shown that $S/I$ is Golod if $\partial(I)^2\subset I$. Here $\partial(I)$ denotes the ideal generated by all the partial derivatives of elements of $I$. We apply this result to find large classes of Golod ideals, including powers, symbolic powers, and saturations of ideals.

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Jürgen Herzog, Craig Huneke. 2012-12-29. Ordinary and symbolic powers are Golod. https://arxiv.org/abs/1212.6579

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