Degenerations to Unobstructed Fano Stanley-Reisner Schemes

Details Degenerations to Unobstructed Fano Stanley-Reisner Schemes Degenerations to Unobstructed Fano Stanley-Reisner Schemes

2011-02-22

arxiv.org/abs/1102.4521v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $T^2$.

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