2003/11/05 by Osamu Fujino, Fujino, Osamu
Mathematics · #14E30 #14M25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14E30 #msc:14M25
paper · pdf · doi:10.48550/arxiv.math/0311068
21 pages; typos were corrected, new remarks were added
openalex publication_date 2003/11/05 · arxiv created 2005/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We treat equivariant completions of toric contraction morphisms as an application of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-\mathbb Q-factorial toric varieties. So, our theory seems to be quite different from Reid's original combinatorial toric Mori theory. We also explain various examples of non-\mathbb Q-factorial contractions, which imply that the \mathbb Q-factoriality plays an important role in the Minimal Model Program. Thus, this paper completes the foundations of the toric Mori theory and show us a new aspect of the Minimal Model Program.