Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves

Details Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves

2004-01-20

arxiv.org/abs/math/0401260v3

Mathematics

Algebraic Geometry

We add a paragraph on the Generalized Gale Transforms. This seems to be what was suggested by Eisenbud and Popescu in [6]

Scientific paper

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.

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