For certain monomial ideals, the paper proposes explicit values and bounds for v-numbers of integral closure filtrations and shows they can be smaller than v-numbers of ordinary powers.
The $\text{v}$-function of powers of sums of ideals
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abstract
Let $K$ be a field, $I\subset R=K[x_1,\dots,x_n]$ and $J\subset T=K[y_1,\dots,y_m]$ be graded ideals. Set $S=R\otimes_KT$ and let $L=IS+JS$. The behaviour of the $\text{v}$-function $\text{v}(L^k)$ in terms of the $\text{v}$-functions $\text{v}(I^k)$ and $\text{v}(J^k)$ is investigated. When $I$ and $J$ are monomial ideals, we describe $\text{v}(L^k)$, giving an explicit formula involving $\text{v}(I^k)$ and $\text{v}(J^k)$.
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math.AC 1years
2025 1verdicts
REJECT 1representative citing papers
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$\operatorname{v}$-numbers of integral closure filtrations of monomial ideals
For certain monomial ideals, the paper proposes explicit values and bounds for v-numbers of integral closure filtrations and shows they can be smaller than v-numbers of ordinary powers.