Monomial degenerations of Mukai Varieties and Fano Threefolds

Rank one index one Fano threefolds of degree up to 18 occur as complete intersections in certain homogeneous spaces known as Mukai varieties. In this talk, I will discuss special degenerations of these Mukai varieties to singular schemes defined by monomial ideals. These degenerations also induce degenerations of the corresponding threefolds for which the special fibers have unobstructed deformations. This allows us to make some conclusions regarding the existence of toric degenerations of Fano threefolds. These results are from joint work with J. Christophersen and V. Przyjalkowski.