A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension. -- Correction by Kenji Matsuki

DOI10.2748/tmj/1178224717zbMath0991.14020OpenAlexW2003724962MaRDI QIDQ1976497

Kenji Matsuki, Dan Abramovich, Suliman Rashid

Publication date: 1 September 2002

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178224717

zbMATH Keywords

birational maps between toric varietiesfactorization of toroidal birational mapsOda's conjecture

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Rational and birational maps (14E05)

Related Items

Boundedness of the space of stable logarithmic maps, Dolbeault cohomology of complex manifolds with torus action, Torification and factorization of birational maps, Toroidal varieties and the weak factorization theorem, Functorial factorization of birational maps for qe schemes in characteristic 0, Local strong factorization of toric birational maps, On Oda's strong factorization conjecture, A point set whose space of triangulations is disconnected, On a logarithmic version of the derived McKay correspondence, Toward the classification of higher-dimensional toric Fano varieties, Tropicalizing the space of admissible covers

Cites Work

• Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
• Toroidal embeddings. I
• The cone of curves of algebraic varieties
• The cone theorem: Note to a paper of Y. Kawamata
• Blow-ups of smooth toric 3-varieties
• Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces
• Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions
• Equivariant completion. II
• Smoothness, semi-stability and alterations
• Local factorization of birational maps
• Equivariant completion
• The Chow rings and GKZ-decompositions for \(\mathbb{Q}\)-factorial toric varieties
• Weak semistable reduction in characteristic 0
• Introduction to Toric Varieties. (AM-131)
• BIRATIONAL GEOMETRY OF TORIC 3-FOLDS
• On the Finiteness of Generators of a Pluri-Canonical Ring for a 3-Fold of General Type
• THE NONVANISHING THEOREM
• Flip Theorem and the Existence of Minimal Models for 3-Folds
• THE GEOMETRY OF TORIC VARIETIES
• Torification and factorization of birational maps
• Decomposition of Birational Toric Maps in Blow-Ups and Blow-Downs
• Threefolds whose canonical bundles are not numerically effective
• Introduction to the Mori program
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item