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PreprintCC BY 4.0arXiv

Intersection Product Formulas and Integral Dependence

  • Yairon Cid-Ruiz
  • Steven Dale Cutkosky
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Abstract

We prove the intersection product formulas of Gaffney and Gassler for polar multiplicities and Segre numbers over arbitrary Noetherian local rings. For equidimensional and universally catenary rings, we give a geometric refinement of the Principle of Specialization of Integral Dependence, in which the maximal dimension of the images of exceptional components mapping into the hypersurface determines a precise Segre number that strictly increases.

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Cite

BibTeXRIS
BibTeX
@misc{cidruiz2026intersection,
  title = {{Intersection Product Formulas and Integral Dependence}},
  author = {Yairon Cid-Ruiz and Steven Dale Cutkosky},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06370},
  eprint = {2611.06370},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06370},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Intersection Product Formulas and Integral Dependence
AU  - Yairon Cid-Ruiz
AU  - Steven Dale Cutkosky
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06370
UR  - https://arxiv.org/abs/2611.06370
AB  - We prove the intersection product formulas of Gaffney and Gassler for polar multiplicities and Segre numbers over arbitrary Noetherian local rings. For equidimensional and universally catenary rings, we give a geometric refinement of the Principle of Specialization of Integral Dependence, in which the maximal dimension of the images of exceptional components mapping into the hypersurface determines a precise Segre number that strictly increases.
ER  -