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On the automorphisms of Mukai varieties

Abstract : Mukai varieties are Fano varieties of Picard number one and coindex three. In genus seven to ten they are linear sections of some special homogeneous varieties. We describe the generic automorphism groups of these varieties. When they are expected to be trivial for dimensional reasons, we show they are indeed trivial, up to three interesting and unexpected exceptions in genera 7, 8, 9, and codimension 4, 3, 2 respectively. We conclude in particular that a generic prime Fano threefold of genus g has no automorphisms for 7 ≤ g ≤ 10. In the Appendix by Y. Prokhorov, the latter statement is extended to g = 12.
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https://hal.archives-ouvertes.fr/hal-03229102
Contributor : Thomas Dedieu Connect in order to contact the contributor
Submitted on : Friday, January 28, 2022 - 3:59:15 PM
Last modification on : Monday, July 4, 2022 - 9:10:44 AM

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  • HAL Id : hal-03229102, version 2
  • ARXIV : 2105.08984

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Thomas Dedieu, Laurent Manivel. On the automorphisms of Mukai varieties. 2022. ⟨hal-03229102v2⟩

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