Deformations of canonical pairs and Fano varieties

DOI10.1515/CRELLE.2011.010zbMath1220.14026arXiv0901.0389OpenAlexW2963282895MaRDI QIDQ3081164

Tommaso de Fernex, Christopher Derek Hacon

Publication date: 11 March 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0389

zbMATH Keywords

rigidityminimal model programdeformations of log pairsMori chamber decompositionsimplicial toric Fano varieties

Mathematics Subject Classification ID

Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items (16)

Quantitative extensions of pluricanonical forms and closed positive currents ⋮ On the relative minimal model program for fourfolds in positive and mixed characteristic ⋮ Extension theorems, non-vanishing and the existence of good minimal models ⋮ K-stability of cubic fourfolds ⋮ Coregularity of Fano varieties ⋮ Arithmetic and geometric deformations of threefolds ⋮ Rigid Gorenstein toric Fano varieties arising from directed graphs ⋮ Fano fourfolds having a prime divisor of Picard number 1 ⋮ Classifying sections of del Pezzo fibrations. I ⋮ On the birational automorphisms of varieties of general type ⋮ A classification of terminal quartic 3-folds and applications to rationality questions ⋮ Jumping of the nef cone for Fano varieties ⋮ K-stability of birationally superrigid Fano varieties ⋮ Product theorem for K-stability ⋮ Manin's \(b\)-constant in families ⋮ On deformations of toric Fano varieties

Cites Work

• Asymptotic cohomological functions of toric divisors
• Higher cohomology of divisors on a projective variety
• On deformation of nef values
• Stratifications de Whitney et théorème de Bertini-Sard
• Invariance of plurigenera
• Degenerations of flag and Schubert varieties to toric varieties
• Mirror symmetry and toric degenerations of partial flag manifolds
• Toric degenerations of spherical varieties
• Pluricanonical systems on algebraic varieties of general type
• Boundedness of pluricanonical maps of varieties of general type
• Existence of minimal models for varieties of log general type
• Existence of minimal models for varieties of log general type II
• Rigidity of the Mori cone for Fano manifolds
• Classification of Three-Dimensional Flips
• Deformations of canonical singularities
• Effective base point freeness
• Mori dream spaces and GIT.

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