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Local resolution of the second log-Fitting ideal

  • Yueting Jiang
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Abstract

Logarithmic Fitting ideals encode the complexity of the corresponding morphisms in a natural and intrinsic way, and their principalisation offers a new perspective on problems such as the resolution of cotangent sheaves and the monomialisation of morphisms. In this paper, we give a local resolution theorem for log-rank adapted morphisms: after finite sequences of smooth local blow-ups, the first two log-Fitting ideals \mathcal{F}_{n−1}(\sigma) and \mathcal{F}_{n−2}(\sigma) become principal monomial ideals.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026local,
  title = {{Local resolution of the second log-Fitting ideal}},
  author = {Yueting Jiang},
  howpublished = {HAL},
  year = {2026},
  month = may,
  doi = {10.48550/arxiv.2611.04723},
  eprint = {2611.04723},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05849129v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Local resolution of the second log-Fitting ideal
AU  - Yueting Jiang
PY  - 2026
DA  - 2026/05/29
PB  - HAL
DO  - 10.48550/arxiv.2611.04723
UR  - https://hal.science/hal-05849129v1
AB  - Logarithmic Fitting ideals encode the complexity of the corresponding morphisms in a natural and intrinsic way, and their principalisation offers a new perspective on problems such as the resolution of cotangent sheaves and the monomialisation of morphisms. In this paper, we give a local resolution theorem for log-rank adapted morphisms: after finite sequences of smooth local blow-ups, the first two log-Fitting ideals \mathcal{F}_{n−1}(\sigma) and \mathcal{F}_{n−2}(\sigma) become principal monomial ideals.
ER  -