On weighted Bergman kernels of bounded domains
We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains for admissible weights .
Optimal destabilizing vectors in some Gauge theoretical moduli problems
We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing -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...
Parabolic exhaustions for strictly convex domains.
Principal Orbit Types for Reductive Groups Acting on Stein Manifolds.
Projective bundles on a complex torus.
Pseudoconcave Lie groups
Pseudokähler forms on complex Lie groups.
Quotienten differenzierbarer und komplexer Räume nach eigentlich-diskontinuierlichen Gruppen.
Quotienten komplexer Mannigfaltigkeiten nach spiegelungsfreien Gruppen.
Realizing countable groups as automorphism groups of Riemann surfaces.
Reductive Group Actions on Stein Spaces.
Reduktive Automorphismengruppen analytischer C-Algebren.
Regularization of birational group operations in sense of Weil.
Rigidity of Holomorphic Self-Mappings and the Automorphism Groups of Hyperbolic Stein Spaces.
Semistable quotients
Singular Holomorphic Representations and Singular Modular Forms.
Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points
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
We study the action of a real-reductive group on a real-analytic submanifold of a Kähler manifold. We suppose that the action of extends holomorphically to an action of the complexified group on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map . We show that almost separates the –orbits if and only if a minimal parabolic subgroup of has an open orbit. This generalizes Brion’s characterization of spherical...
Spherical Stein manifolds and the Weyl involution
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...
Stability of meromorphic vector fields in projective spaces.