Abstract
In this work, we improve results of (Ressayre in Geometric invariant theory and generalized eigenvalue problem II, pp 1–25 2008; Ressayre in Ann. Inst. Fourier. 180:389–441 2010) on GIT-cones associated to the action of a reductive group G on a projective variety X. These results are applied to give a short proof of the Derksen–Weyman theorem that parametrizes bijectively the faces of a rational cone associated to any quiver without oriented cycles. An important example of such a cone is the Horn cone.
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The author was supported by the French National Research Agency (ANR-09-JCJC-0102-01).
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Ressayre, N. GIT-cones and quivers. Math. Z. 270, 263–275 (2012). https://doi.org/10.1007/s00209-010-0796-0
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DOI: https://doi.org/10.1007/s00209-010-0796-0