On surfaces in P⁴ and 3-folds in P⁵
classification
alg-geom
math.AG
keywords
foldssmoothsurfacesexamplesadjunctionarisingclassificationconstruct
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This is a survey on the classification of smooth surfaces in P^4 and smooth 3-folds in P^5. 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 P^4 and 3-folds in P^5 known to us.
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