On Calabi-Yau varieties that are linear sections of Grassmannians of lines

@misc{bolognesi2026calabiyau,
  title = {{On Calabi-Yau varieties that are linear sections of Grassmannians of lines}},
  author = {Michele Bolognesi and Ciro Ciliberto and Alessandro Verra},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11925},
  eprint = {2610.11925},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11925},
}

TY  - UNPB
TI  - On Calabi-Yau varieties that are linear sections of Grassmannians of lines
AU  - Michele Bolognesi
AU  - Ciro Ciliberto
AU  - Alessandro Verra
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11925
UR  - https://arxiv.org/abs/2610.11925
AB  - In this paper we consider the n−3 dimensional linear section X_Π of the Grassmannian 𝔾(1,n) of lines in ℙ^n with a general linear space Π of codimension n+1, with n=2k+1 odd and n≥ 5, that is a Calabi-Yau variety. Related to X_Π there is a degree k+1 Pfaffian hypersurface 𝒞_Π that is the intersection of the dual of 𝔾(1,n) with Π^⊥. We prove that 𝒞_Π is rational and we provide a birational parametrization of it. Moreover we study in some detail the congruence of lines of ℙ^n given by the centers of the linear complexes parametrised by the points of 𝒞_Π.
ER  -