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On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds

  • Xiaolong Liu
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Abstract

In this paper, we study logarithmic Donaldson-Thomas invariants for local log Calabi-Yau $4$-folds with simple normal crossing divisors. Using the family version of shifted Lagrangian classes announced by Khan-Kinjo-Park-Safronov, we construct relative and family logarithmic DT4-theories for logarithmic Hilbert schemes of curves, and prove a degeneration formula. For logarithmic Hilbert schemes of points, we construct virtual classes and prove a degeneration formula in Chow groups; in particular, it is independent of shifted Lagrangian classes. Finally, combining our degeneration formula with logarithmic cobordism, we explicitly compute the zero-dimensional logarithmic DT4-invariants for local surface snc pairs.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026logarithmic,
  title = {{On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds}},
  author = {Xiaolong Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17720},
  eprint = {2609.17720},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17720},
}
RIS
TY  - UNPB
TI  - On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds
AU  - Xiaolong Liu
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.17720
UR  - https://arxiv.org/abs/2609.17720
AB  - In this paper, we study logarithmic Donaldson-Thomas invariants for local log Calabi-Yau $4$-folds with simple normal crossing divisors. Using the family version of shifted Lagrangian classes announced by Khan-Kinjo-Park-Safronov, we construct relative and family logarithmic DT_4-theories for logarithmic Hilbert schemes of curves, and prove a degeneration formula. For logarithmic Hilbert schemes of points, we construct virtual classes and prove a degeneration formula in Chow groups; in particular, it is independent of shifted Lagrangian classes. Finally, combining our degeneration formula with logarithmic cobordism, we explicitly compute the zero-dimensional logarithmic DT_4-invariants for local surface snc pairs.
ER  -