Non-abelian LVM manifolds}

@misc{seade2026nonabelian,
  title = {{Non-abelian LVM manifolds}},
  author = {José Seade},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25368},
  eprint = {2610.25368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25368},
}

TY  - UNPB
TI  - Non-abelian LVM manifolds}
AU  - José Seade
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25368
UR  - https://arxiv.org/abs/2610.25368
AB  - We extend the tangency construction of López de Medrano, Verjovsky and Meersseman from diagonal abelian actions to non-abelian Samelson groups. For these groups the tangency locus is a moment-map zero set: the commutator term in the leafwise Hessian vanishes there, and under an admissibility hypothesis, Kempf--Ness convexity gives a global transversal whose projectivization is a compact complex manifold. The construction includes compact rotation groups and groups with non-closed central rotations. In the latter setting we construct explicit families of complex dimension 2m−3, m≥5, which are $4$-connected and admit no symplectic form. Their meromorphic function fields are rational of transcendence degree m−2, although every holomorphic map to a projective space is constant. We compute their connected automorphism groups and show that they admit no maximal torus action. They are Hopf-surface bundles over compact complex quotients of stable Grassmannian loci; these bases give related examples already in complex dimension five. The families demonstrate that the non-abelian tangency construction reaches beyond compact complex manifolds with maximal torus actions.
ER  -