Mathematical Sciences: Complex Manifold Theory and Kaehler Geometry

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DMS-9500999 Siu Siu will investigate several related problems in complex manifold theory and Kaehler geometry. These include hyperbolicity problems, effective freeness and very ampleness, general Bochner type formula and geometric superrigidity, and global nondeformability of compact hermitian symmetric manifolds. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.