Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 34 min ago
PreprintarXiv licencearXiv

A semiampleness result for hyperkähler fourfolds and smoothings of Lagrangian subvarieties

  • Andreas Höring
  • Vladimir Lazić
  • Christian Lehn
Open at sourcePDFDOICite

Abstract

We give a geometric proof of the following statement: let X be a smooth hyperkähler fourfold such that the Picard group is generated by a line bundle L that is nef, non-trivial, and not big. If the Kodaira dimension of L is non-negative, some positive multiple defines a Lagrangian fibration. The proof requires a number of tools which are of independent interest, including an analogue of Voisin's unobstructedness result and a smoothing result for singular Lagrangian subvarieties.

Related

  1. Lagrangian fibrations on hyperkahler manifolds have no multiple fibers in codimension one
    Ljudmila Kamenova, Misha Verbitsky
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Semiampleness on Jacobian elliptic surfaces of Kodaira dimension one
    Antonio Laface, Sichen Li
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Normal complex surface singularities with rational homology disk smoothings
    Márton Beke, Heesang Park, Dongsoo Shin +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Convergence of spectral smoothings from compact quantum group actions
    Trevor Camper, Dimitrios Giannakis, Gage Hoefer
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. Weighted homogeneous surface singularities admitting rational homology disk smoothings
    Heesang Park, Dongsoo Shin
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{horing2026semiampleness,
  title = {{A semiampleness result for hyperkähler fourfolds and smoothings of Lagrangian subvarieties}},
  author = {Andreas Höring and Vladimir Lazić and Christian Lehn},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31497},
  eprint = {2610.31497},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31497},
}
RIS
TY  - UNPB
TI  - A semiampleness result for hyperkähler fourfolds and smoothings of Lagrangian subvarieties
AU  - Andreas Höring
AU  - Vladimir Lazić
AU  - Christian Lehn
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31497
UR  - https://arxiv.org/abs/2610.31497
AB  - We give a geometric proof of the following statement: let X be a smooth hyperkähler fourfold such that the Picard group is generated by a line bundle L that is nef, non-trivial, and not big. If the Kodaira dimension of L is non-negative, some positive multiple defines a Lagrangian fibration. The proof requires a number of tools which are of independent interest, including an analogue of Voisin's unobstructedness result and a smoothing result for singular Lagrangian subvarieties.
ER  -