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Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry

Laurent Bruasse, Andrei Teleman (2005)

Annales de l’institut Fourier

We give here a generalization of the theory of optimal destabilizing 1-parameter subgroups to non algebraic complex geometry : we consider holomorphic actions of a complex reductive Lie group on a finite dimensional (possibly non compact) Kähler manifold. In a second part we show how these results may extend in the gauge theoretical framework and we discuss the relation between the Harder-Narasimhan filtration and the optimal detstabilizing vectors of a non semistable object....

Hölder continuous solutions to Monge–Ampère equations

Jean-Pierre Demailly, Sławomir Dinew, Vincent Guedj, Pham Hoang Hiep, Sławomir Kołodziej, Ahmed Zeriahi (2014)

Journal of the European Mathematical Society

Let ( X , ω ) be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on X with L p right hand side, p > 1 . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range ( X , ω ) of the complex Monge-Ampère operator acting on ω -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with L p -density belong to ( X , ω ) and proving that ( X , ω ) has the...

Holomorphic Poisson Cohomology

Zhuo Chen, Daniele Grandini, Yat-Sun Poon (2015)

Complex Manifolds

Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients in...

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