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Prime Fano fourfolds in classical and generalized Grassmannians

  • Alessandro Frassineti
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Abstract

We provide a complete classification of Fano fourfolds of Picard rank 1 and index 1 obtained as zero loci of completely reducible homogeneous vector bundles in generalized Grassmannians, i.e. Grassmannians of Dynkin type different from A. This extends the classification done by Küchle in standard Grassmannians. In doing so, we exhibit three new families of Fano fourfolds of Picard rank 1 and index 1. For each of the studied Fano fourfolds, we compute several numerical invariants, such as volume and Hodge numbers.

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Cite

BibTeXRIS
BibTeX
@misc{frassineti2026prime,
  title = {{Prime Fano fourfolds in classical and generalized Grassmannians}},
  author = {Alessandro Frassineti},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09310},
  eprint = {2609.09310},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09310},
}
RIS
TY  - UNPB
TI  - Prime Fano fourfolds in classical and generalized Grassmannians
AU  - Alessandro Frassineti
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09310
UR  - https://arxiv.org/abs/2609.09310
AB  - We provide a complete classification of Fano fourfolds of Picard rank 1 and index 1 obtained as zero loci of completely reducible homogeneous vector bundles in generalized Grassmannians, i.e. Grassmannians of Dynkin type different from A. This extends the classification done by Küchle in standard Grassmannians. In doing so, we exhibit three new families of Fano fourfolds of Picard rank 1 and index 1. For each of the studied Fano fourfolds, we compute several numerical invariants, such as volume and Hodge numbers.
ER  -