Year: 2026
Type: preprint
Abstract: In this paper, we study the ${\rm v}$-number of the symbolic-ordinary discrepancy modules $M_t(I) = I^{(t)} / I^t$ over standard graded Noetherian rings. We show that this coincides with the ${\rm v}$-number of $I^t$ at embedded primes. Moreover, under mild assumptions on $I$, we show that the ${\rm v}$-number of $N_t(I) = I^{(t)} / I^{(t+1)}$ is the same as the ${\rm v}$-number of $I^{(t+1)}$. Furthermore, we provide combinatorial formulas for these ${\rm v}$-numbers when $t = 2, 3$ and $I$ is the edge ideal of a graph. Consequently, we classify all graphs for which ${\rm v}(I^2) = {\rm v}(I^{(2)})$.
Source: arXiv (Cornell University)
Authors: Kumar, Manohar, Minh, Nguyen Cong, Vu, Thanh
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214034237