On the automorphisms of Mukai varieties

Thomas Dedieu (1) , Laurent Manivel (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Géométrie algébrique [math.AG]

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