2006/09/24 by Michel Brion, Brion, Michel · 4 citations
Computer Science · Mathematics · #14L30 #14M17 #32M10 #32M12 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14L30 #msc:14M17 #msc:32M10 #msc:32M12
paper · pdf · doi:10.48550/arxiv.math/0609669
Final version, to appear in the Proceedings of the VI Coloquio Latinoamericano de Algebra (Colonia, Uruguay, 2005)
openalex publication_date 2006/09/24 · arxiv created 2007/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a complete nonsingular algebraic variety X and a divisor D with normal crossings, we say that X is log homogeneous with boundary D if the logarithmic tangent bundle TX(- log D) is generated by its global sections. We then show that the Albanese morphism α is a fibration with fibers being spherical (in particular, rational) varieties. It follows that all irreducible components of D are nonsingular, and any partial intersection of them is irreducible. Also, the image of X under the morphism σ associated with - KX - D is a spherical variety, and the irreducible components of all fibers of σ are quasiabelian varieties. Generalizing the Borel-Remmert structure theorem for homogeneous varieties, we show that the product morphism α× σ is surjective, and the irreducible components of its fibers are toric varieties. We reduce the classification of log homogeneous varieties to a problem concerning automorphism groups of spherical varieties, that we solve under an additional assumption.