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The GIT-Equivalence for G-Line Bundles

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Abstract

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 Thaddeus and Dolgachev-Hu.

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Authors and Affiliations

  1. Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques, Université de Grenoble I, BP 74, 38402, Saint Martin D'Hères Cedex, France

    N. Ressayre

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  1. N. Ressayre
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Ressayre, N. The GIT-Equivalence for G-Line Bundles. Geometriae Dedicata 81, 295–324 (2000). https://doi.org/10.1023/A:1005275524522

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