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PreprintCC BY-NC-ND 4.0arXiv

Asymptotic GIT-stability of KSB-stable varieties

  • Sándor J Kovács
  • Behrouz Taji
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Abstract

We prove that KSB-stable varieties introduced by Kollár and Shepherd-Barron as a generalization of Deligne-Mumford's stable curves are stable in the sense of geometric invariant theory (GIT). More precisely, we show that KSB-stable varieties are asymptotically GIT-stable with respect to a sequence of linearizations defined by the Hodge bundle.

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Cite

BibTeXRIS
BibTeX
@misc{kovacs2026asymptotic,
  title = {{Asymptotic GIT-stability of KSB-stable varieties}},
  author = {Sándor J Kovács and Behrouz Taji},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40583},
  eprint = {2610.40583},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40583},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Asymptotic GIT-stability of KSB-stable varieties
AU  - Sándor J Kovács
AU  - Behrouz Taji
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40583
UR  - https://arxiv.org/abs/2610.40583
AB  - We prove that KSB-stable varieties introduced by Kollár and Shepherd-Barron as a generalization of Deligne-Mumford's stable curves are stable in the sense of geometric invariant theory (GIT). More precisely, we show that KSB-stable varieties are asymptotically GIT-stable with respect to a sequence of linearizations defined by the Hodge bundle.
ER  -