Degenerations to unobstructed Fano Stanley–Reisner schemes

Abstract

We construct degenerations of Mukai varieties and linear sections thereof to special unobstructed Fano Stanley–Reisner schemes corresponding to convex deltahedra. This can be used to find toric degenerations of rank one index one Fano threefolds. Furthermore, we show that the Stanley–Reisner ring of the boundary complex of the dual polytope of the associahedron has trivial $$T^2$$ . This can be used to find new toric degenerations of linear sections of $$G(2,n)$$ .