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INTEGRAL CLOSURE OF STRONGLY GOLOD IDEALS

  • CĂTĂLIN CIUPERCĂ (a1)

Abstract

We prove that the integral closure of a strongly Golod ideal in a polynomial ring over a field of characteristic zero is strongly Golod, positively answering a question of Huneke. More generally, the rational power $I_{\unicode[STIX]{x1D6FC}}$ of an arbitrary homogeneous ideal is strongly Golod for $\unicode[STIX]{x1D6FC}\geqslant 2$ and, if $I$ is strongly Golod, then $I_{\unicode[STIX]{x1D6FC}}$ is strongly Golod for $\unicode[STIX]{x1D6FC}\geqslant 1$ . We also show that all the coefficient ideals of a strongly Golod ideal are strongly Golod.

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