MORSE THEORY WITH THE NORM-SQUARE OF A HYPERKAHLER MOMENT MAP
نویسندگان
چکیده
منابع مشابه
Morse Theory with the Norm-square of a Hyperkähler Moment Map
We prove that the norm-square of a moment map associated to a linear action of a compact group on an affine variety satisfies a certain gradient inequality. This allows us to bound the gradient flow, even if we do not assume that the moment map is proper. We describe how this inequality can be extended to hyperkähler moment maps in some cases, and use Morse theory with the norm-squares of hyper...
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The main results of this manuscript concern the Morse theory associated to the norm-square of a Kähler moment map f = ‖Φ − α‖2 on the space of representations Rep(Q,v) of a quiver; these are the first steps in a larger research program concerning the hyperkähler analogue of the well-known Kirwan surjectivity theorem in symplectic geometry. The first main result is that, although ‖Φ − α‖2 is not...
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The first seven sections of the paper contain a version of localization for the normsquare of the moment map in equivariant de Rham theory. Similar results are proved by P.-E. Paradan in [30], [31], [32]; our statement and method of proof are somewhat different. The existence of such a formula was first suggested by Witten [39], see also Jeffrey and Kirwan [19]. A K-theory version is given by V...
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We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat’s proof is an adaptation of Lojasiewicz’s argument for analytic functions to functions which are locally analytic.
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Let X be any nonsingular complex projective variety with a linear action of a complex reductive group G, and let X and X be the sets of semistable and stable points of X in the sense of Mumford’s geometric invariant theory [17]. We can choose a maximal compact subgroup K of G and an inner product on the Lie algebra k of K which is invariant under the adjoint action. Then X has a G-equivariantly...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2013
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/has045