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Mathematics > Algebraic Geometry

arXiv:math/0401260 (math)
[Submitted on 20 Jan 2004 (v1), last revised 1 Apr 2004 (this version, v3)]

Title:Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves

Authors:Yi Hu
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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.
Comments: We add a paragraph on the Generalized Gale Transforms. This seems to be what was suggested by Eisenbud and Popescu in [6]
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG)
Cite as: arXiv:math/0401260 [math.AG]
  (or arXiv:math/0401260v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.math/0401260

Submission history

From: Yi Hu [view email]
[v1] Tue, 20 Jan 2004 18:23:45 UTC (27 KB)
[v2] Tue, 27 Jan 2004 18:44:58 UTC (27 KB)
[v3] Thu, 1 Apr 2004 23:03:47 UTC (27 KB)
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