Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 58 min ago
PreprintarXiv licencearXiv

Free abelian group actions on projective fibered varieties

  • Sichen Li
Open at sourcePDFDOICite

Abstract

Let X be an n-dimensional normal projective variety of Kodaira dimension κ and G an abelian subgroup of automorphisms such that all elements of Gbackslash {id} are of positive entropy. Dinh and Sibony showed that G is actually free abelian of rank ≤ n−κ−1. In this paper, we show that after replacing G by a finite-index subgroup, there exists a G-Equivariant Minimal Model Program for the pair $(X, G)$ when rank(G)=n−κ−1 and κ>0, and the very general fiber of the final model is a klt Calabi-Yau surface or a Q-abelian variety provided that the termination of flips holds in this setting.

Related

  1. Post-quantum commutative group actions from oriented superspecial abelian varieties
    Wouter Castryck, Bogdan Adrian Dina, Péter Kutas +1
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv
  2. Continuous graph homomorphisms of higher dimensional abelian group actions
    Ruijun Wang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsLogic & foundationsarXiv
  3. On a Combinatorial Characterization of Abelian Group Actions
    Carson Gull, Arthur Illidge, Benjamin Mudrak +2
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Hyperbolicity and fundamental groups of complex quasi-projective varieties (III): applications
    Benoit Cadorel, Ya Deng, Katsutoshi Yamanoi
    HALPreprintPublisher termsFull textAlgebra & number theoryAnalysis & PDEsHAL
  5. Dynamical degrees of automorphisms on abelian varieties
    Nguyen-Bac Dang, Thorsten Herrig
    Advances in MathematicsPeer-reviewedHAL deposit licenceFull text6 citedAlgebra & number theoryHAL

Cite

BibTeXRIS
BibTeX
@misc{li2026free,
  title = {{Free abelian group actions on projective fibered varieties}},
  author = {Sichen Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25778},
  eprint = {2610.25778},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25778},
}
RIS
TY  - UNPB
TI  - Free abelian group actions on projective fibered varieties
AU  - Sichen Li
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25778
UR  - https://arxiv.org/abs/2610.25778
AB  - Let X be an n-dimensional normal projective variety of Kodaira dimension κ and G an abelian subgroup of automorphisms such that all elements of Gbackslash {id} are of positive entropy. Dinh and Sibony showed that G is actually free abelian of rank ≤ n−κ−1. In this paper, we show that after replacing G by a finite-index subgroup, there exists a G-Equivariant Minimal Model Program for the pair $(X, G)$ when rank(G)=n−κ−1 and κ>0, and the very general fiber of the final model is a klt Calabi-Yau surface or a Q-abelian variety provided that the termination of flips holds in this setting.
ER  -