Abstract
In this paper we show that there are no smooth rational 3-folds in ℙ5 (C) which are rational conic bundles, over minimal surfaces, whose generic fibre is embedded as a rational curve of degreeh≥3, (ifh=2 there is a complete classification for these 3-folds as well as for the case of ℙ1-bundles). Except for conic bundles, we also give the complete list of rational 3-folds in ℙ5 which are minimal according to Mori’s theory. These are little steps towards the classification of all smooth 3-folds in ℙ5 not of general type.
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