Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles [PDF]
Épijournal de Géométrie Algébrique, 2022 For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics.
Yoshinori Hashimoto, Julien Keller
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Kobayashi—Hitchin correspondence for twisted vector bundles
Complex Manifolds, 2021 We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds.
Perego Arvid
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Polystable bundles and representations of their automorphisms
Complex Manifolds, 2022 Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kähler manifold are shown to be (poly)stable if and only if their corresponding classes are (poly)stable in the sense of
Buchdahl Nicholas, Schumacher Georg
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Existence of approximate Hermitian-Einstein structures on semistable principal bundles [PDF]
, 2012 Let E_G be a principal G-bundle over a compact connected K\"ahler manifold, where G is a connected reductive complex linear algebraic group. We show that E_G is semistable if and only if it admits approximate Hermitian-Einstein structures.Comment: 7 ...
Adam Jacob +9 more
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Applications of the Ashtekar gravity to four dimensional hyperk\"ahler geometry and Yang-Mills Instantons [PDF]
, 1996 The Ashtekar-Mason-Newman equations are used to construct the hyperk\"ahler metrics on four dimensional manifolds. These equations are closely related to anti self-dual Yang-Mills equations of the infinite dimensional gauge Lie algebras of all volume ...
Gava E. +7 more
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A Kähler Einstein structure on the tangent bundle of a space form
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 3, Page 183-195, 2001., 2001 We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive ...
Vasile Oproiu
wiley +1 more source
Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains [PDF]
, 2015 It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite dimensional inner product spaces.
Koranyi, Adam, Misra, Gadadhar
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A note on the index bundle over the moduli space of monopoles
, 1994 Donaldson has shown that the moduli space of monopoles $M_k$ is diffeomorphic to the space $\Rat_k$ of based rational maps from the two-sphere to itself.
C.H. Taubes +11 more
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The geometric sense of R. Sasaki connection
, 2002 For the Riemannian manifold $M^{n}$ two special connections on the sum of the tangent bundle $TM^{n}$ and the trivial one-dimensional bundle are constructed. These connections are flat if and only if the space $M^{n}$ has a constant sectional curvature $\
Alexey V Shchepetilov +9 more
core +4 more sources
Uniform L2-estimates for flat nontrivial line bundles on compact complex manifolds
Complex ManifoldsIn this study, we extend the uniform L2{L}^{2}-estimate of ∂¯\bar{\partial }-equations for flat nontrivial line bundles, proved for compact Kähler manifolds by Hashimoto and Koike, to compact complex manifolds.
Hashimoto Yoshinori +2 more
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