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Classification of can-Var diagrams of mixed Hodge structures and monodromic mixed Hodge modules on ℂ

  • Takahiro Saito
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Abstract

By our previous work, the category of unipotent monodromic mixed Hodge modules on ℂ is equivalent to the category of can-Var diagrams of mixed Hodge structures. In this paper, we show that the associated graded diagram with respect to the weight filtrations decomposes as a finite direct sum of four basic types tensored with pure Hodge structures, which we call a split graded model. We then show that every unipotent monodromic mixed Hodge module is represented by a split graded model together with a finite family of ℂ-linear maps. We also obtain an analogous description in the case where the monodromy has no eigenvalue $1$.

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Cite

BibTeXRIS
BibTeX
@misc{saito2026classification,
  title = {{Classification of can-Var diagrams of mixed Hodge structures and monodromic mixed Hodge modules on $\mathbbC$}},
  author = {Takahiro Saito},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13192},
  eprint = {2610.13192},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13192},
}
RIS
TY  - UNPB
TI  - Classification of can-Var diagrams of mixed Hodge structures and monodromic mixed Hodge modules on ℂ
AU  - Takahiro Saito
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13192
UR  - https://arxiv.org/abs/2610.13192
AB  - By our previous work, the category of unipotent monodromic mixed Hodge modules on ℂ is equivalent to the category of can-Var diagrams of mixed Hodge structures. In this paper, we show that the associated graded diagram with respect to the weight filtrations decomposes as a finite direct sum of four basic types tensored with pure Hodge structures, which we call a split graded model. We then show that every unipotent monodromic mixed Hodge module is represented by a split graded model together with a finite family of ℂ-linear maps. We also obtain an analogous description in the case where the monodromy has no eigenvalue $1$.
ER  -