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 degree h≥3, (if h=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.
On the non existence of some rational 3-folds in P^5 / A. Alzati. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - 40:1(1994 Dec), pp. 55-70. [10.1007/BF02834512]
On the non existence of some rational 3-folds in P^5
A. AlzatiPrimo
1994
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 degree h≥3, (if h=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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