Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 2 min ago
PreprintarXiv licencearXiv

v-numbers of symbolic-ordinary discrepancy modules

  • Manohar Kumar
  • Nguyen Cong Minh
  • Thanh Vu
Open at sourcePDFDOICite

Abstract

In this paper, we study the v-number of the symbolic-ordinary discrepancy modules Mt(I) = I(t) / It over standard graded Noetherian rings. We show that this coincides with the v-number of It at embedded primes. Moreover, under mild assumptions on I, we show that the v-number of Nt(I) = I(t) / I(t+1) is the same as the v-number of I(t+1). Furthermore, we provide combinatorial formulas for these v-numbers when t = 2, 3 and I is the edge ideal of a graph. Consequently, we classify all graphs for which v(I2) = v(I(2)).

Related

  1. Comparisons between ordinary and symbolic powers of edge ideals with respect to regularity and depth
    Yuji Muta
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. A Sensitivity-based Framework for Calibrating Coupled Ordinary Differential Equations under Model Discrepancy
    Mitchel J. Colebank, William Consagra
    arXivPreprintCC BY-NC-SA 4.0Full textOptimisation & controlStatisticsarXiv
  3. Ordinary modules for affine vertex operator superalgebras
    Huaimin Li, Qing Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Trivial Iwasawa modules and arithmetic linking numbers
    Yasushi Mizusawa, Keiji Okano
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. The Tate Conjecture for Ordinary Calabi-Yau Threefolds
    Lukas Brantner
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{kumar2026vnumbers,
  title = {{v-numbers of symbolic-ordinary discrepancy modules}},
  author = {Manohar Kumar and Nguyen Cong Minh and Thanh Vu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.22872},
  eprint = {2609.22872},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22872},
}
RIS
TY  - UNPB
TI  - v-numbers of symbolic-ordinary discrepancy modules
AU  - Manohar Kumar
AU  - Nguyen Cong Minh
AU  - Thanh Vu
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.22872
UR  - https://arxiv.org/abs/2609.22872
AB  - In this paper, we study the 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 v-number of I^t at embedded primes. Moreover, under mild assumptions on I, we show that the v-number of N_t(I) = I^(t) / I^(t+1) is the same as the v-number of I^(t+1). Furthermore, we provide combinatorial formulas for these v-numbers when t = 2, 3 and I is the edge ideal of a graph. Consequently, we classify all graphs for which v(I^2) = v(I^(2)).
ER  -