The GIT-equivalence for $G$-line bundles
| dc.creator | Ressayre, Nicolas | |
| dc.date | 1998-11-09 | |
| dc.date.accessioned | 2026-07-07T05:26:47Z | |
| dc.date.available | 2026-07-07T05:26:47Z | |
| dc.description | Let $X$ be a projective variety with an action of a reductive group $G$. Each ample $G$-line bundle $L$ on $X$ defines an open subset $X^{\rm ss}(L)$ of semi-stable points. Following Dolgachev and Hu, define a GIT-class as the set of algebraic equivalence classes of $L'$s with fixed $X^{\rm ss}(L)$. We show that the GIT-classes are the relative interiors of rational polyhedral convex cones, which form a fan in the $G$-ample cone. We also study the corresponding variations of quotients $X^{\rm ss}(L)//G$. This sharpens results of Thaddeus and Dolgachev-Hu. | |
| dc.description | 36 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/9811053 | |
| dc.identifier | http://arxiv.org/abs/math/9811053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77680 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The GIT-equivalence for $G$-line bundles | |
| dc.type | text |