Hilbert schemes and toric degenerations for low degree Fano threefolds

DOI10.1515/crelle-2014-0011zbMath1445.14006arXiv1202.0510OpenAlexW3103663961MaRDI QIDQ305152

Jan Arthur Christophersen, Nathan Owen Ilten

Publication date: 29 August 2016

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.0510

zbMATH Keywords

Hilbert schemesFano threefoldsreflexive polytopestoric degenerations

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Parametrization (Chow and Hilbert schemes) (14C05) Families, moduli, classification: algebraic theory (14J10) Fano varieties (14J45)

Related Items

Hilbert schemes and toric degenerations for low degree Fano threefolds ⋮ Versality in toric geometry ⋮ Equivariant vector bundles on \(t\)-varieties ⋮ Degenerations to unobstructed Fano Stanley-Reisner schemes ⋮ From cracked polytopes to Fano threefolds ⋮ Cracked polytopes and Fano toric complete intersections ⋮ On toric geometry and K-stability of Fano varieties ⋮ On deformations of toric Fano varieties

Uses Software

• Macaulay2
• 4ti2
• TOPCOM
• Graded Ring Database
• VersalDeformations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum periods for 3-dimensional Fano manifolds
• Hilbert schemes and toric degenerations for low degree Fano threefolds
• Toric degenerations of Fano threefolds giving weak Landau-Ginzburg models
• Degenerations to unobstructed Fano Stanley-Reisner schemes
• Cotangent cohomology of Stanley-Reisner rings
• Torus embeddings and tangent complexes
• Classification of Fano 3-folds with \(B_ 2 \geq 2\)
• Classification of reflexive polyhedra in three dimensions
• Versal deformations and local Hilbert schemes
• Weak Landau-Ginzburg models for smooth Fano threefolds
• Mirror Symmetry and Fano Manifolds
• Deformations of Algebraic Schemes
• Deformations of graded algebras.
• Hyperelliptic and trigonal Fano threefolds
• Combinatorics and commutative algebra
• Rolling factors deformations and extensions of canonical curves
• Deforming Stanley-Reisner schemes