Explicit formula for regularity of almost complete intersection monomial ideals and proof that integral closure regularity is bounded by the original for dominant and almost complete intersection cases.
A counterexample to a conjecture of K\"uronya and Pintye on regularity and integral closure
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We exhibit an equigenerated monomial ideal $I\subseteq K[x,y,z,w]$ with $\operatorname{reg}(\overline{I})>\operatorname{reg}(I)$. The ideal $I$ is generated in degree 4 and satisfies $\operatorname{reg}(I)=4$, while its integral closure $\overline{I}$ has a minimal generator of degree 5 and satisfies $\operatorname{reg}(\overline{I})=5$. This gives a counterexample to the polynomial-ring formulation of the K\"uronya--Pintye conjecture.
fields
math.AC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
On the Regularity of Dominant and Almost Complete Intersection Monomial Ideals
Explicit formula for regularity of almost complete intersection monomial ideals and proof that integral closure regularity is bounded by the original for dominant and almost complete intersection cases.