Counterexamples to the $I^{(3)} \subset I^2$ containment

preprint2015arXivOpen access

We show that in general the third symbolic power of a radical ideal of points in the complex projective plane is not contained in the second usual power of that ideal. This answers in negative a question asked by Huneke and generalized by Harbourne.

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Counterexamples to the $I^{(3)} \subset I^2$ containment

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Counterexamples to the I(3)⊂I2I^{(3)} \subset I^2I(3)⊂I2 containment

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Counterexamples to the $I^{(3)} \subset I^2$ containment