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Tangent scrolls in prime Fano threefolds

Atanas Iliev·Carmen Schuhmann
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Abstract

In this paper we prove that any smooth prime Fano threefold, different from the Mukai-Umemura threefold, contains a 1-dimensional family of intersecting lines. Combined with a result of the second author (see J. Algebr. Geom. 8:2 (1999), 221-244) this implies that any morphism from a smooth Fano threefold of index 2 to a smooth Fano threefold of index 1 must be constant, which gives an answer in dimension 3 to a question stated by Peternell.

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Atanas Iliev, Carmen Schuhmann. 2000-05-04. Tangent scrolls in prime Fano threefolds. https://arxiv.org/abs/math/0005040

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