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. In the second part we find many higher dimensional unobstructed Fano and Calabi-Yau Stanley-Reisner schemes. The main result is that the Stanley-Reisner ring of the boundary complex of the dual polytope of the associahedron has trivial $T^2$.

v2: 24 pages, 5 figures. Major revision to v1 with many new results. Parts of v1 have been moved to the preprint "Toric Degenerations of Low Degree Fano Threefolds"

References in corpus (2)

• On G-Fano threefolds
• Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models

Cited by in corpus (7)

• Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
• Laurent Inversion
• On deformations of toric Fano varieties
• Cracked Polytopes and Fano Toric Complete Intersections
• Unobstructed Stanley-Reisner Degenerations for Dual Quotient Bundles on $G(2,n)$
• Singularities and radical initial ideals
• Deformation Theory for Finite Cluster Complexes