Tangent scrolls in prime Fano threefolds
Algebraic Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/0005040,
title = {Tangent scrolls in prime Fano threefolds},
author = {Atanas Iliev and Carmen Schuhmann},
journal= {arXiv preprint arXiv:math/0005040},
year = {2007}
}
Comments
19 pages, Latex