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PreprintCC BY-NC-ND 4.0arXiv

A general Lê--Siersma formula

  • R. Giménez Conejero
  • J. J. Nuño-Ballesteros
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Abstract

We consider the comparison between a Milnor fibre of a function f and its section by the zero locus of a second function s in a general ambient variety 𝒳. We give a formula that generalizes those of Lê and Siersma, expressing the difference of their Euler characteristics as a sum of local contributions associated with the critical points of the restriction of s. We provide an algebraic formula in the case that 𝒳 is {smooth of pure dimension outside f−1(0)}, and show some applications and examples.

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Cite

BibTeXRIS
BibTeX
@misc{conejero2026general,
  title = {{A general Lê--Siersma formula}},
  author = {R. Giménez Conejero and J. J. Nuño-Ballesteros},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06340},
  eprint = {2611.06340},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06340},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A general Lê--Siersma formula
AU  - R. Giménez Conejero
AU  - J. J. Nuño-Ballesteros
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06340
UR  - https://arxiv.org/abs/2611.06340
AB  - We consider the comparison between a Milnor fibre of a function f and its section by the zero locus of a second function s in a general ambient variety 𝒳. We give a formula that generalizes those of Lê and Siersma, expressing the difference of their Euler characteristics as a sum of local contributions associated with the critical points of the restriction of s. We provide an algebraic formula in the case that 𝒳 is {smooth of pure dimension outside f^−1(0)}, and show some applications and examples.
ER  -