An equigenerated monomial ideal in K[x,y,z,w] provides a counterexample to the Küronya-Pintye conjecture by satisfying reg(¯I)=5 > reg(I)=4.
Javadekar,A comparison of the regularity of certain classes of monomial ideals and their integral closures, Archiv der Mathematik126(2026), 351–363
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A counterexample to a conjecture of K\"uronya and Pintye on regularity and integral closure
An equigenerated monomial ideal in K[x,y,z,w] provides a counterexample to the Küronya-Pintye conjecture by satisfying reg(¯I)=5 > reg(I)=4.