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PreprintCC BY 4.0arXiv

Gepner stability conditions on hypersurface categories

  • Anibal Aravena
  • Peize Liu
  • Jenia Tevelev
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Abstract

We construct numerical Bridgeland stability conditions on the category of graded matrix factorizations of every smooth complex projective hypersurface of degree d≥2. These conditions are of Gepner type (τ,2/d), where τ is the grading shift autoequivalence. By Orlov's theorem, this gives stability conditions of Gepner type on all Calabi--Yau hypersurfaces and on Kuznetsov components of all Fano hypersurfaces. These conditions satisfy a mass-Hom bound and the support property on the full numerical Grothendieck group. Semistable objects of fixed numerical class and phase admit proper good moduli spaces.

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Cite

BibTeXRIS
BibTeX
@misc{aravena2026gepner,
  title = {{Gepner stability conditions on hypersurface categories}},
  author = {Anibal Aravena and Peize Liu and Jenia Tevelev},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05350},
  eprint = {2611.05350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05350},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Gepner stability conditions on hypersurface categories
AU  - Anibal Aravena
AU  - Peize Liu
AU  - Jenia Tevelev
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05350
UR  - https://arxiv.org/abs/2611.05350
AB  - We construct numerical Bridgeland stability conditions on the category of graded matrix factorizations of every smooth complex projective hypersurface of degree d≥2. These conditions are of Gepner type (τ,2/d), where τ is the grading shift autoequivalence. By Orlov's theorem, this gives stability conditions of Gepner type on all Calabi--Yau hypersurfaces and on Kuznetsov components of all Fano hypersurfaces. These conditions satisfy a mass-Hom bound and the support property on the full numerical Grothendieck group. Semistable objects of fixed numerical class and phase admit proper good moduli spaces.
ER  -