# The GIT-Equivalence for G-Line Bundles

```@article{Ressayre1998TheGF,
title={The GIT-Equivalence for G-Line Bundles},
author={Nicolas Ressayre},
journal={Geometriae Dedicata},
year={1998},
volume={81},
pages={295-324}
}```
• N. Ressayre
• Published 9 November 1998
• Mathematics
• Geometriae Dedicata
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 Xss(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 XssL. 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 Xss(L)//G. This sharpens results of…
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