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On weighted Bergman kernels of bounded domains

Sorin Dragomir (1994)

Studia Mathematica

We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains Ω ⊂ ℂ N for admissible weights a ∈ L ¹ ( Ω ) .

Optimal destabilizing vectors in some Gauge theoretical moduli problems

Laurent Bruasse (2006)

Annales de l’institut Fourier

We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing 1 -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...

Semistable quotients

Peter Heinzner, Luca Migliorini, Marzia Polito (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points

Roger Bielawski (2017)

Complex Manifolds

We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of GL(n, ℂ) is isomorphic to the deformation of the D2-singularity if n = 2, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if n = 3, and to the Atiyah-Hitchin manifold itself if n = 4. For higher n, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on one of the above surfaces....

Spherical gradient manifolds

Christian Miebach, Henrik Stötzel (2010)

Annales de l’institut Fourier

We study the action of a real-reductive group G = K exp ( 𝔭 ) on a real-analytic submanifold X of a Kähler manifold. We suppose that the action of G extends holomorphically to an action of the complexified group G ℂ on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map μ 𝔭 : X → 𝔭 . We show that μ 𝔭 almost separates the K –orbits if and only if a minimal parabolic subgroup of G has an open orbit. This generalizes Brion’s characterization of spherical...

Spherical Stein manifolds and the Weyl involution

Dmitri Akhiezer (2009)

Annales de l’institut Fourier

We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical subgroups...

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