Klt varieties with semipositive anticanonical bundle : symmetric tensors, holonomy and structure

Abstract

The aim of this article is to study klt projective varieties such that the anticanonical bundle is semipositive from the differential-geometric point of view. The study of the holonomy of such varieties yields generalizations of several results. We show that the dimension of the space of symmetric differentials is bounded by a constant depending on the augmented irregularity, generalizing a result of Kobayashi. If we endow such a variety X with a metric ω whose Ricci curvature is non-negative, then we show that the holonomy of the regular locus is compact. If we assume that X has canonical singularities, then we show that the general fiber of the Albanese map can be decomposed into a product of irreducible Calabi-Yau varieties, irreducible holomorphic symplectic varieties and hereditarily rationally connected varieties by the holonomy generalizing a structure theorem of Campana, Demailly and Peternell. To conclude, we show that the fundamental group of the regular locus of such varieties is virtually abelian.

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BibTeX RIS

BibTeX

@misc{dailly2026varieties,
  title = {{Klt varieties with semipositive anticanonical bundle : symmetric tensors, holonomy and structure}},
  author = {Louis Dailly},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37002},
  eprint = {2610.37002},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37002},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Klt varieties with semipositive anticanonical bundle : symmetric tensors, holonomy and structure
AU  - Louis Dailly
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37002
UR  - https://arxiv.org/abs/2610.37002
AB  - The aim of this article is to study klt projective varieties such that the anticanonical bundle is semipositive from the differential-geometric point of view. The study of the holonomy of such varieties yields generalizations of several results. We show that the dimension of the space of symmetric differentials is bounded by a constant depending on the augmented irregularity, generalizing a result of Kobayashi. If we endow such a variety X with a metric ω whose Ricci curvature is non-negative, then we show that the holonomy of the regular locus is compact. If we assume that X has canonical singularities, then we show that the general fiber of the Albanese map can be decomposed into a product of irreducible Calabi-Yau varieties, irreducible holomorphic symplectic varieties and hereditarily rationally connected varieties by the holonomy generalizing a structure theorem of Campana, Demailly and Peternell. To conclude, we show that the fundamental group of the regular locus of such varieties is virtually abelian.
ER  -

Abstract

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