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An asymptotic Γ-BMT inequality

  • Nick Rekuski
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Abstract

We refine a bound of Cheng-Feyzbakhsh to prove an asymptotic Γ-Bayer-Macrì-Toda (Γ-BMT) inequality on every smooth polarized complex threefold. The proof relies on a reduction to small tilt stability parameters. Using this inequality we verify Feyzbakhsh-Thomas's condition (wBG) whenever KX is numerically proportional to the polarization. For polarized Calabi-Yau threefolds, this yields a reduction of positive rank generalized Donaldson-Thomas (DT) invariants to those counting sheaves pure in codimension one. We further express these invariants in terms of rank one generalized DT invariants. Thus, the rank reductions of Feyzbakhsh-Thomas hold without assuming the BMT conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{rekuski2026asymptotic,
  title = {{An asymptotic $Γ$-BMT inequality}},
  author = {Nick Rekuski},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31399},
  eprint = {2610.31399},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31399},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - An asymptotic Γ-BMT inequality
AU  - Nick Rekuski
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31399
UR  - https://arxiv.org/abs/2610.31399
AB  - We refine a bound of Cheng-Feyzbakhsh to prove an asymptotic Γ-Bayer-Macrì-Toda (Γ-BMT) inequality on every smooth polarized complex threefold. The proof relies on a reduction to small tilt stability parameters. Using this inequality we verify Feyzbakhsh-Thomas's condition (wBG) whenever K_X is numerically proportional to the polarization. For polarized Calabi-Yau threefolds, this yields a reduction of positive rank generalized Donaldson-Thomas (DT) invariants to those counting sheaves pure in codimension one. We further express these invariants in terms of rank one generalized DT invariants. Thus, the rank reductions of Feyzbakhsh-Thomas hold without assuming the BMT conjecture.
ER  -