K‐stable Fano threefolds of rank 2 and degree 28

Abstract Moduli spaces of Fano varieties have historically been difficult to construct. However, recent work has shown that smooth K‐polystable Fano varieties of fixed dimension and volume can be parametrised by a quasi‐projective moduli space. In this paper, we prove that all smooth Fano threefolds with Picard rank 2 and degree 28 are K‐polystable, except for some explicit cases which we describe.