Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

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DMS-9500491 Shiffman Shiffman will continue his research on complex varieties and meromorphic mappings. He will investigate the Kabayashi-Royden infinitesimal pseudometric and Kobayashi pseudodistane with a goal towards obtaining a better understanding of the concept of hyperbolicity for projective manifolds. He will also return to the topic of value distribution theory and will seek new defect relations for meromorphic maps and for sections of vector bundles. 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.