On surfaces in P⁴ and 3-folds in P⁵

1994/02/08 by Wolfram Decker, Sorin Popescu, Decker, Wolfram +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9402006

24 pages, AMS-TeX 2.1

arxiv created 1994/02/08 · arxiv updated 2009/11/30

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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• Syzygies of Abelian and Bielliptic Surfaces in P⁴
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• Threefolds in \Bbb P⁵ with a 3-dimensional family of plane curves