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Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves | | Yi Hu
; | | Date: |
20 Dec 2003 | | Subject: | Algebraic Geometry; Differential Geometry | math.AG math.DG | | Abstract: | In this paper we provide some stability criteria for systems of linear subspaces of $V otimes W$ and for systems of quotient coherent sheaves, using, respectively, the Hilbert-Mumford numerical criterion and moment map. Along the way, we generalize the Gelfand-MacPherson correspondence [11] from point sets to sets of linear subspaces (of various dimensions). And, as an application, we provide some examples of $G$-ample cones without any top chambers. The results of this paper are based upon and/or generalize some earlier works of Klyachko [18], Totaro [28], Gelfand-MacPherson [11], Kapranov [17], Foth-Lozano [8], Simpson [24], Wang [30], Phong-Sturm [22], Zhang [32] and Luo [20], among others. | | Source: | arXiv, math.AG/0401260 | | Services: | Forum | Review | PDF | Favorites | |
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