Analysis shows that integral closures have equal or lower regularity than original monomial ideals, confirming a key conjecture.
Let S = k[x₁, …, xₙ], I be an ideal of S, and Ī denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal I of S, the inequality reg(Ī) ≤ reg(I) holds, where reg(₎ denotes the Castelnuovo-Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals.
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Omkar Javadekar (2025) studied this question.
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