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Global boundary regularity for the p a r t i a l ¯ -equation on q -pseudo-convex domains

Heungju Ahn (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For a bounded domain D of C n , we introduce a notion of « q -pseudoconvexity» of new type and prove that for a given ¯ -closed p , r -form f that is smooth up to the boundary on D , and for r q , there exists a p , r - 1 -form u smooth up to the boundary on D which is a solution of the equation ¯ u = f

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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