Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 32 min ago
PreprintarXiv licencearXiv

Finite Symplectic Automorphisms of Hyperkähler Manifolds of K3[n]-Type Act Trivially on Discriminant Groups

  • Jie Fu
  • Shihao Wang
  • Zhiwei Zheng
Open at sourcePDFDOICite

Abstract

We give an alternative proof of Mongardi's result that every finite group of symplectic automorphisms of a hyperkähler manifold of K3[n]-type acts trivially on the discriminant groups of its second cohomology lattice and its coinvariant lattice. The proof combines sphere-packing bounds, Vinberg's reflection chambers and structure results on even $2$-elementary lattices.

Related

  1. Dynamical degrees of automorphisms of non-projective hyperkähler manifolds
    Eva Bayer-Fluckiger, Stevell Muller, Matthias Schütt
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. A Proof of Mongardi's Conjecture on Finite Symplectic Group Actions on Hyperkähler Manifolds of K3[n] Type
    Jie Fu, Shihao Wang, Zhiwei Zheng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Symplectic singularity as hyperKähler cone
    Yuji Odaka
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  4. Second Chern class and Fujiki constants of hyperkähler manifolds
    Thorsten Beckmann, Jieao Song
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryPeer-reviewedLicence not statedFull text13 citedGeometry & topologyOpenAlex
  5. Geometric quantizazion and TYCZ coefficients of HyperKähler 4-manifolds
    Simone Cristofori
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{fu2026finite,
  title = {{Finite Symplectic Automorphisms of Hyperkähler Manifolds of $K3^[n]$-Type Act Trivially on Discriminant Groups}},
  author = {Jie Fu and Shihao Wang and Zhiwei Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35916},
  eprint = {2610.35916},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35916},
}
RIS
TY  - UNPB
TI  - Finite Symplectic Automorphisms of Hyperkähler Manifolds of K3^[n]-Type Act Trivially on Discriminant Groups
AU  - Jie Fu
AU  - Shihao Wang
AU  - Zhiwei Zheng
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.35916
UR  - https://arxiv.org/abs/2610.35916
AB  - We give an alternative proof of Mongardi's result that every finite group of symplectic automorphisms of a hyperkähler manifold of K3^[n]-type acts trivially on the discriminant groups of its second cohomology lattice and its coinvariant lattice. The proof combines sphere-packing bounds, Vinberg's reflection chambers and structure results on even $2$-elementary lattices.
ER  -