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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.28712 |
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Table of Contents:
- We construct prime Fano manifolds from spin representations of $Spin_n$ for $n\le 14$. In this range, and if $n\ne 13$, the projectivizations of these representations are prehomogeneous, and we deduce that our Fano manifolds are locally rigid and, up to a few exceptions, quasi-homogeneous under the action of their automorphism groups. For $n=13$ we obtain a non-trivial family of minimal compactifications of $SL_3\times SL_3$, modulo some finite group.