On surfaces in P4 and 3-folds in P5
Abstract
This is a survey on the classification of smooth surfaces in P4 and smooth 3-folds in P5. We recall the corresponding results arising from adjunction theory and explain how to construct examples via syzygies. We discuss some examples in detail and list all families of smooth non-general type surfaces in P4 and 3-folds in P5 known to us.
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