A note on scrolls of smallest embedded codimension

1995/07/07 by Takao Fujita, Fujita, Takao
Mathematics · #14J60 (Primary) 14J40 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG #msc:14J40 #msc:14J60

paper · pdf · doi:10.48550/arxiv.alg-geom/9507003

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arxiv created 1995/07/11 · arxiv updated 2009/11/30

Abstract

Let M be a submanifold of \Bbb P^N of dimension n>2. Suppose that (M,\Cal O_M(1))≅\Bbb P(\Cal E),\Cal O(1)) for some vector bundle \Cal E on a surface S. Then N≥ 2n-1 by Barth-Lefschetz Theorem. We are interested in the case N=2n-1. In 1994 Ionescu and Toma gave a classification of the cases where S is not of general type. Here we propose a conjecture concerning this remaining case, which is verified for n≤ 1100 by a computer programm.

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