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Motivic local density of isolated singularities of algebraic varieties

  • Sidonie Ratajczak
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Abstract

The goal of this paper is to compute the motivic local density of an isolated singularity of an algebraic variety, in order to explain its link with algebraic multiplicity. We compute the density as the residue in 1 of a Zeta function associated to normalized local volumes and we use a resolution of the singularity to get the formula.

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Cite

BibTeXRIS
BibTeX
@misc{ratajczak2026motivic,
  title = {{Motivic local density of isolated singularities of algebraic varieties}},
  author = {Sidonie Ratajczak},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32416},
  eprint = {2610.32416},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32416},
}
RIS
TY  - UNPB
TI  - Motivic local density of isolated singularities of algebraic varieties
AU  - Sidonie Ratajczak
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32416
UR  - https://arxiv.org/abs/2610.32416
AB  - The goal of this paper is to compute the motivic local density of an isolated singularity of an algebraic variety, in order to explain its link with algebraic multiplicity. We compute the density as the residue in 1 of a Zeta function associated to normalized local volumes and we use a resolution of the singularity to get the formula.
ER  -