Log homogeneous varieties
| dc.creator | Brion, Michel | |
| dc.date | 2006-09-24 | |
| dc.date | 2007-01-24 | |
| dc.date.accessioned | 2026-07-07T07:42:38Z | |
| dc.date.available | 2026-07-07T07:42:38Z | |
| dc.description | 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 $T_X(- \log D)$ 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 $- K_X - D$ 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 $α\times σ$ 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. | |
| dc.description | Final version, to appear in the Proceedings of the VI Coloquio Latinoamericano de Algebra (Colonia, Uruguay, 2005) | |
| dc.identifier | https://arxiv.org/abs/math/0609669 | |
| dc.identifier | http://arxiv.org/abs/math/0609669 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122513 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L30, 14M17, 32M10, 32M12 | |
| dc.title | Log homogeneous varieties | |
| dc.type | text |