Hilbert Schemes and Toric Degenerations for Low Degree Fano Threefolds

Abstract

For fixed degree $d\le 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties to toric Fano varieties with at most canonical Gorenstein singularities.

24 pages, 2 figures; v2 simplified exposition by using rolling factors format where applicable; v3 further revisions to exposition, changed title

References in corpus (2)

• Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
• VersalDeformations - a package for computing versal deformations and local Hilbert schemes

Cited by in corpus (4)

• On toric geometry and K-stability of Fano varieties
• On deformations of toric Fano varieties
• Cracked Polytopes and Fano Toric Complete Intersections
• Deformation Theory for Finite Cluster Complexes